Publications
of R.D. Lazarov by Years
| 2008
| 2007 | 2006 | 2005
| 2004 | 2003 | 2002
| 2001 | 2000 | 1999
| 1998 | 1997 | 1996
| 1995 | 1994 | 1993
| 1992 | 1991 | 1990
| 1989 | 1988 | 1987
| 1986 | 1985 | 1984
| 1983 | 1982 | 1981
| 1980 | 1979 | 1978
| 1977 | 1976 | 1975
| 1974 | 1973 | 1972
| 1971 |
2008
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V.A. Dobrev, R.D. Lazarov, and L.T. Zikatanov,
Preconditioning of symmetric interior penalty discontinuous Galerkin FEM for
second order elliptic problems , In
Domain Decomposition Methods Science and Enginering XVII,
Lecture Notes in Computational Science and Engineering, vol. 60, U. Langer et al. eds,
Springer-Verlag, Berlin, Heidelberg, pp. 33--44 (2008).
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R. Lazarov, S. Repin, and S. Tomar, Functional a posteriori error estimates for
discontinuous Galerkin approximations of elliptic problems,
accepted in J. Numerical Methods for PDEs, (December 2007).
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B. Cockburn, J. Gopalakrishnan, and R. Lazarov,
Unified hybridization of discontinuous Galerkin, mixed, and conforming methods
for second-order elliptic problems
sumitted to SINUM , (December 2007).
2007
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P. Chatzipantelidis, R. Lazarov, and V. Tomee,
Parabolic finite volume element equations in nonconvex polygonal domains,
ISC Technical Reports, ISC-07-08-MATH,
Institute for Scientific Computation,
submited to J. Numerical Methods for PDEs, (October 2007).
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R.D. Lazarov and S.D. Margenov,
CBS constants for graph-Laplacians and application to multilevel
methods for discontinuous Galerkin systems,
Joural of Complexity ,
23 (4-6) (2007), 498--515
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R.D. Lazarov, S. Lu, and S.V. Pereverzev,
On the balancing principle for some problems of numerical analysis,
Numerische Mathematik , 106 (4) (2007), 659-689
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O. Iliev, R. Lazarov, J. Willems,
Numerical study of two-grid preconditioners for 1-D elliptic
problems with highly oscillating discontinuous coefficients,
Computational Methods in Applied Mathematics, 7 (1) (2007), 48-67
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R.E. Ewing, O.P. Iliev, R.D. Lazarov, and A. Naumovich,
On convergence of certain finite volume difference discretizations for
1-D poroelasticity interface problems,
Numer. Methods for Partial Differential Equations,
23 (3) (2007), 652-671
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R.D. Lazarov and X. Ye,
Stabilized discontinuous finite element approximations for Stokes equations,
J. Comput. Appl. Math., 198 (1) (2007), 236-252
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K. Kachiashvili, D. Gordeziani, R. Lazarov and D. Melikdzhanian,
Modeling and simulation of pollutants transport in rivers,
Applied Mathematical Modelling,
31 (7) (2007) 1371-1396
2006
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P. Chatzipantelidis, R.D. Lazarov, V. Thomee, and L. Wahlbin,
Parabolic finite element equations in convex polygonal domains,
BIT Numerical Mathematics. 43 (Suppl. 1) 2006, S113-S143
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V.A. Dobrev, R.D. Lazarov, P.S. Vassilevski, and L.T. Zikatanov,
Two-level preconditioning of discontinuous Galerkin approximations of
second order elliptic equations,
Numer. Linear Algebra Appl.,
13 (9) (2006), 753--770
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C.C. Douglas, C. Harris, J., Iskandarani, M., Johnson, C.R., Lodder, R.J.,
Parker, S.G., Cole, M.J., Ewing, R., Efendiev, Y., Lazarov, R., Qin, G.,
Dynamic contaminant identification in water,
ICCS 2006: Proc. 6-th International Conference, Part III,
Lecture Notes in Computer Science, 3993, (2006), 393-400
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A. Andreev, R. Lazarov, M. Racheva,
Postprocessing and Improved Accuracy of the Lowest-Order Mixed Finite
Element Approximation for Biharmonic Eigenproblems,
Lecture Notes in Computer Science, 3743 , (2006) 613-620
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R. Sinha, R.E. Ewing, and R.D. Lazarov,
Some new error estimates of a semidiscrete finite volume element method for
parabolic integro-differential equation with nonsmooth initial data,
SIAM J. Numer.Anal., 43 (6) (2006), 2320-2344.
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C. Douglas, Y. Efendiev, R. Ewing, V. Ginting, and R. Lazarov,
Dynamic data driven simulations in stochastic environments,
Computing, 77 (4) (2006), 321-332
2005
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R.D. Lazarov and L.T. Zikatanov,
An exponential fitting scheme for general convection-diffusion equations on
tetrahedral meshes,
Technical Report ISC-04-15-MATH , Texas A& M University,
Comput. Appl. Math., (Obchysljuval'na ta prykladna matematyka, Kiev)
1(92) , (2005), 60-69
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A.B. Andreev, R.D. Lazarov, and M.R. Racheva,
Postprocessing and Higher Order Convergence of Mixed Finite Element
Approximations of Biharmonic Eigenvalue Problems,
also as
Technical Report ISC-04-04-MATH , Texas A& M University,
J. Comput. Appl. Math., 182 (2) (2005), 333-349
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C.C. Douglas, Y. Efendiev, R.E. Ewing, V. Ginting,
R.D. Lazarov, M.J. Cole, G. Jones,
Least-squares approach for data recovery in dynamic data-driven applications simulations,
to appear in Journal of Computing and Visualization in Science ,
submitted November (2004)
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C.C. Douglas, Y. Efendiev, R.E. Ewing, V. Ginting, R.D. Lazarov,
M.J. Cole, G. Jones, and C.R. Johnson,
Multiscale Interpolation, Backward in Time Error Analysis for Data-Driven
Contaminant Simulation , ICCS 2005, V.S. Sunderam et al.(Eds),
Lecture Notes in Computer Science , 3515, (2005), 640-647
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P. Chatzipantelidis, V. Ginting, and R.D. Lazarov,
A finite volume element method for nonlinear elliptic problems,
Numer. Linear Algebra Appl., 12 (2005), 515-546
(also
Technical Report ISC-04-06-MATH , (2004), Texas A& M University)
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P. Chatzipantelidis and R.D. Lazarov,
Error estimates for
finite volume element method for elliptic PDE's in nonconvex polygonal domains,
SIAM J. Numer.Anal.
42 (5) (2005) 1932 -- 1958 (also
Technical Report ISC-03-04-MATH , (2003), Texas A& M University).
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C. Carstensen, R.D. Lazarov, and S. Tomov,
Explicit and averaging a posteriori error estimates for adaptive
finite volume methods,
SIAM J. Numer.Anal.
42 (6) (2005) 2496-2521
2004
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A. Kurganov, R. Lazarov, D. Levy, G. Petrova, and B. Popov,
Eitan Tadmor - 50,
Comput. Meth. Appl. Math., 4 (3) (2004), 265-270
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P. Chatzipantelidis, R.D. Lazarov, and V. Thomee,
Error estimates for the finite volume
element method for parabolic equations in convex polygonal domains ,
Numer. Methods for Partial Diff. Equations, 20 (5) (2004), 650-674
also as
Technical Report ISC-03-03-MATH , (2003), Texas A& M University)
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Y. Efendiev, R.E. Ewing, V. Ginting, and R.D. Lazarov,
Upscaling modeling in muliphase flow applications,
J. Computational and Applied Mathematics,
23 (2-3) (2004) 213--233
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R. Sinha and R. Lazarov,
A new technique for error analysis of finite element approximations of
parabolic problems with non-smooth initial data ,
Approximation Theory, A volume dedicated to B.Bojanov
(D.K.Dimitrov, G. Nikolov, and R. Uluchev, Eds),
Prof. M. Drinov Academic Publishing House, Sofia, 2004, pp. 296-308
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C. C. Douglas, C. Shannon, Y. Efendiev, R. Ewing, V. Ginting,
R. Lazarov, M. R. Cole, G. Jones, C. R. Johnson, and J. Simpson,
Using a virtual telemetry methodology for dynamic data driven application simulations,
(to appear in Dynamic Data Driven Applications Systems, F. Darema (ed.),
Kluwer, Amsterdam, 2004, 16 pp.
PDF
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C.C. Douglas, C.E. Shannon, Y. Efendiev, R.E. Ewing, V. Ginting, R.D. Lazarov,
M.J. Cole, G. Jones, C.R. Johnson and J. Simpson,
A Note on Data-Driven Contaminant Simulation , Computational Science - ICCS 2004,
Lecture Notes in Computer Science, 3038, (2004), 701-708
2003
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C.C. Douglas, Y. Efendiev, R. Ewing, R.D. Lazarov, M.J. Cole, G. Jones, C.R. Johnson,
Virtual telemetry for dynamic data-driven application simulations, Springer
Lect. Notes in Comp. Sci., 2660 , (2003) 279-288.
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R.D. Lazarov, J.E. Pasciak, J. Schoberl, and P.S. Vassilevski,
Almost optimal interior penalty discontinuous approximation
of symmetric elliptic problems on non-matching grids,
Numerische Mathematik, 96 (2) , (2003) 295-315
(also as
Technical Report ISC-02-06-MATH, Texas A& M University)
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C. C. Douglas, M. R. Cole, Y. Efendiev, R. Ewing, V. Ginting, G. Jones,
C. R. Johnson, R. Lazarov, C. Shannon, and J. Simpson,
A note on dynamic data driven application simulation (DDDAS) using virtual telemetry,
Proc. ICPACE 2003, J. Zou and X. Chi (eds.),
Chinese University of Hong Kong, 2003, pp. 193-198.
PostScript
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R.D. Lazarov and S. Margenov,
On a two-level parallel MIC(0) preconditioning of
Crouzeix-Raviart non-conforming FEM systems ,
Springer
Lecture Notes in Computer Science , 2542 , (2003) 192--204
(also as
Technical Report ISC-02-06-MATH , Texas A& M University)
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C.C. Douglas, Y. Efendiev, R.E. Ewing, R.D. Lazarov,
M.R. Cole, C.R. Johnson, and G. Jones,
Virtual telemetry middleware for DDD Application Simulations,
P.M.A. Sllot et al, (Eds.), ICC 2003, Part 4,
Springer
Lecture Notes in Computer Science 2660 (2003), pp. 279-288.
2002
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V.A. Dobrev, R.E. Ewing, R.D. Lazarov, and J.E. Pasciak,
Numerical study of the performance of preconditioners based
on algebraic multigrid method and approximate sparse inverses,
Technical Report ISC-02-07-MATH, Texas A& M University, 2002.
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P. Chatzipantelidis and R.D. Lazarov,
The finite volume element method in nonconvex domains,
Finite Volumes for Complex Applications III, R. Herbin and D. Kroner, Eds,
Hermes Penton Science, 2002, 171 - 178.
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T.I. Chernogorova, R.E. Ewing, O.P. Iliev, and R.D. Lazarov,
On finite volume discretzation of elliptic interface problem,
Finite Volumes for Complex Applications III, R. Herbin and D. Kroner, Eds,
Hermes Penton Science, 2002, 301 - 308.
-
R.D. Lazarov, Bramble-Hilbet lemma,
In: Supplement 3 of the Encyclopaedia of Mathematics ,
Kluwer Academic Publishers, 2002, pp. 79 - 81.
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R.D. Lazarov and P.S. Vassilevski,
Numerical methods for convection-diffusion problems on general grids,
Technical Report ISC-02-01-MATH, Texas A& M University,
In: Approximation Theory: A volume dedicated to Blagovest Sendov,
B. Bojanov (Ed.), Darba, Sofia, 2002, 258 - 283.
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R.D. Lazarov and S.Z. Tomov,
A posteriori error estimates for finite volume element
approximations of convection-diffusion-reaction equations,
Comput. Geosciences, 6 (3-4) (2002) 483 - 503
(also as
Technical Report ISC-00-02-MATH , Texas A& M University)
2001
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- R.D. Lazarov,
J.E. Pasciak, and P.S. Vassilevski,
Iterative
solution of a conbined mixed and standard Galerkin discretization method for
elliptic problems,
Numer.
Linear Algebra Appl., 8 (2001), 13-31.
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J.H. Bramble, R.D. Lazarov, and J.E. Pasciak,
Least-squares methods for linear elasticity based on a discrete minus
one inner product,
Technical Report ISC-99-05-MATH, Texas A&M University ,
Computer Meth. Appl. Mech. Engrg., 191 (8-10)
(2001), 727-744
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R.D. Lazarov, S.Z. Tomov, and P.S. Vassilevski,
Interior penalty discontinuous approximations of elliptic problems,
Technical Report ISC-00-04-MATH, Texas A& M University
Comput. Method Appl. Math.,
1 (4) (2001), 367-382.
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C. Kim, R.D. Lazarov, J.E. Pasciak, and P.S. Vassilevski,
Multiplier spaces for the mortar finite element method in three dimensions,
SIAM Numer. Anal.
, 39 (2) (2001), 519-538.
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R.E. Ewing, A. Ibragimov, and R.D. Lazarov,
Domain decomposition algorithm
and analytical simulation of coupled flow in reservoir/well system,
J. KSIAM
, 5 (2) (2001), 71--99.
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R.D. Lazarov and S.Z. Tomov,
Adaptive finite volume
element method for convection-diffusion-reaction problems in 3-D,
Scientific Computing and Application (Eds, P. Minev and Y. Lin)
Advances in Computation: Theory and Practice,
Nova Science Publishing House, 7 (2001), 91--106
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R.E. Ewing, O. Iliev, and R.D. Lazarov,
A modified finite volume approximation of second-order elliptic
equations with discontinuous coefficients,
Technical Report, ISC-99-01-MATH,
SIAM Sci. Comput., 23 (4) (2001), 1334-1350.
2000
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- R.D. Lazarov,
J.E. Pasciak, and P.S. Vassilevski,
Mixed
finite element methods for elliptic problems on non--matching grids,
Notes on Numerical Fluid Mechanics, 73 (2000), 25-35.
- R.E. Ewing,
R.D. Lazarov, and Y. Lin,
Finite
volume element approximation of nonlocal reactive flows in porous media,
Numer. Methods for Partial Diff. Equations, 16(3) (2000), 285-311.
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T. Chernogorova, R.E. Ewing, O.P. Iliev, and R.D. Lazarov,
On the discretization of interface problems with perfect and imperfect contact,
Lecture Notes in Physics, Springer-Verlag, New York,552(2000),
93-103.
- R.E. Ewing,
R.D. Lazarov, T. Lin, and Y. Lin,
Mortar
finite volume element approximations of second order elliptic problems,
East-West
J. Numer. Math, 8(2), (2000), 93-110.
- R.E. Ewing,
R.D. Lazarov, and Y. Lin,
Finite
volume element approximations of non-local in time one-dimensional flows in
porous media,
Computing , 64 (2000), 157-182.
- R.E. Ewing,
A. Ibragimov, and R.D. Lazarov,
3-D
simulation of the pressure drop along horizontal wells in a bounded reservoir,
Proceedings of the Fourth Conference on Horizontal Well Technology,
SPE, SPE65505 (2000) (CD-ROM/Internet publication).
- R.D. Lazarov
and P.S. Vassilevski,
Least-squares streamline diffusion finite element approximations to
singularly perturbed convection-diffusion problems,
Analytical and Numerical Methods for
Singularly Perturbed Problems, (L.G. Vulkov, J.J.H. Miller, and G.I.
Shishkin, Eds.), Nova Science Publishing House, 2000, pp.83--94.
- R.D. Lazarov,
J.E. Pasciak, and S.Z. Tomov,
Error control, local grid refinement, and efficient solution algorithms for
singularly perturbed problems,
Analytical and Numerical Methods for Singularly
Perturbed Problems (L.G. Vulkov, J.J.H. Miller, and G.I. Shishkin, Eds.),
Nova Science Publishing House, 2000, pp. 71--82.
- R.D. Lazarov
and S.Z. Tomov, Tool-box for parallel simulation of flows in porous media,
Proc. Cross Discipline Ecosystem Modeling and Analysis Workshop, U.S.
EPA, Research Triangle Park, 2000, pp. 27-28.
1999
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- R.E. Ewing,
R.D. Lazarov, S.L. Lyons, D.V. Papavassiliou, J.E. Pasciak, and G. Qin,
Numerical well model
for non-Darcy flow through isotropic porous media,
Computational Geosciences,
3 (3,4) (1999), 185-204.
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R.E. Ewing, R.D. Lazarov, T. Lin, and Y. Lin,
Domain
decomposition capabilities for the mortar finite volume element methods,
Proceedings of the 11th International Conference on Domain Decomposition
Methods (Choi-Hong Lai, Petter E. Bjorstad, Mark Cross, and Olof B. Widlund,
Eds.), Bergen, Domain Decomposition Press, (1999), 220-227.
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R.D. Lazarov, J.E. Pasciak, and P.S. Vassilevski,
Coupling mixed and finite volume discretizations of
convection-diffusion-reaction equations on non-matching grids,
Finite Volumes for Complex Applications II.
Problems and Perspectives, (R. Vilsmeier, F. Benkhaldoun, and D. Hanel
Eds.), Hermes Science Publications, Paris, 1999, 51 - 68.
- R.E. Ewing,
R.D. Lazarov, and Y. Lin,
Finite
volume element approximations of integro-differential parabolic problems,
Recent Adavances in Numerical Methods and Applications (O. Iliev,
M. Kaschiev, S. Margenov, Bl. Sendov, P. Vassilevski, Eds.),
World Scientific, 1999, 3--15.
1998
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J.H. Bramble, R.D. Lazarov, and J.E. Pasciak,
Least-Squares for second order elliptic problems,
Comp. Meth. Appl. Mech. Engng., 152 (1998), 195-210.
- R.E. Ewing,
R.D. Lazarov, and H. Chen,
Superconvergence
of the mixed finite element methods for parabolic problems with non-smooth
initial data, Numerische
Mathematik, 78 (1998), 495-521.
1997
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- J.H. Bramble,
R.D. Lazarov, and J.E. Pasciak,
A least-squares
approach based on a discrete minus one inner Product for first order systems,
Math. Comp., 66,
(1997), 935--955.
- R.D. Lazarov,
L. Tobiska, and P.S. Vassilevski,
Streamline
diffusion least-squares mixed finite element methods for convection-diffusion
problems,
East-West J. Numer. Math. , 5, (1997), 249 -- 264.
- H. Chen, R.E. Ewing,
and R.D. Lazarov,
Asymptotic error expansion for the
lowest order Raviat-Thomas rectangular mixed finite elements,
Technical Report, ISC-97-01-MATH, 1997, 1 -- 11.
1996
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- Z. Chen, R.E.
Ewing, Yu.A. Kuznetsov, R.D. Lazarov, and S. Maliassov,
Multilevel
preconditioners for mixed methods for second order elliptic problems,
Numer. Lin.
Alg. with Appl., 3(5) (1996), 427-453.
- Z. Chen, R.E.
Ewing, and R.D. Lazarov,
Domain
decomposition algorithms for mixed methods for second order elliptic problems,
Math. Comp., 65(214)
(1996), 467-490.
- R.D. Lazarov
and P.S. Vassilevski,
Preconditioning saddle-point
problems arising from mixed finite element discretizations of elliptic equations,
Numer.
Lin. Algebra Appl. , 3(1) (1996) 1-20.
- R.D. Lazarov,
I.D. Mishev, and P.S. Vassilevski,
Finite volume
methods for convection-diffusion problems,
SIAM J. Numer. Anal., 33(1) (1996) 31-55.
- R.E. Ewing,
R.D. Lazarov, J.E. Pasciak, and A.T. Vassilev, Mathematical modeling, Numerical
Techniques, and Computer Simulation of flows and transport in porous media,
Proc. Comput. Techniques and Applications: CTAC95, World Scientific, Singapore,
1996, 13-30.
- H. Chen and
R.D. Lazarov, Domain splitting
algorithm for mixed finite element approximations to parabolic problems,
East-West J. Numer. Math. , 4, (1996), 121-135.
- R.D. Lazarov
and I.D. Mishev, Finite
volume methods for reaction-diffusion problems, Proc. First Intern.
Symposium on Finite Volume Methods for Complex Applications (F. Benkhaldoun
and R. Vilsmeier, Eds.), Hermes Publishers, 1996, pp. 233 - 240.
1995
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- H. Chen and
R.D. Lazarov, Error analysis
of fully discrete mixed finite element approximations to parabolic problems,
Technical Report ISC-95-06-MATH, Institute for Scientific Computation,
Texas A&M University, 1995.
- R.E. Ewing,
R.D. Lazarov, J.E. Pasciak, and A.T. Vassilev,
Computational
techniques in multiphase flow and transport in porous media, Proceedings
International Conference on Mathematics and Computations, Reactor Physics
and Environmental Analysis, American Nuclear Society, (1995), 414-420.
1994
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- H.
Chen,
R.E. Ewing, and R.D. Lazarov,
Superconvergence
of the mixed finite element approximations to parabolic equations,
Advances in Numerical Methods and Applications O(h3) (I.T. Dimov, Bl. Sendov,
and P.S. Vassilevski, eds.), World Scientific, Singapore, (1994), 63-69.
- R.E. Ewing,
Yu.A. Kuznetsov, R.D. Lazarov, and S. Maliassov,
Preconditioning
of nonconforming finite element approximations of second order elliptic problems,
Advances in Numerical Methods and Applications O(h3) (I.T. Dimov, Bl. Sendov,
and P.S. Vassilevski, Eds.), World Scientific, Singapore, (1994), 101-110.
- R.E. Ewing,
Yu.A. Kuznetsov, R.D. Lazarov, and S. Maliassov,
Substructuring
preconditioning for finite element approximations of second order elliptic
problems, I. Nonconforming linear elements for the Poisson equation in a parallelepiped,
IMA Preprint #1280, University of Minnesota, Minneapolis, (1994).
- R.E. Ewing
and R.D. Lazarov, Approximation
of parabolic problems on grids locally refined in time and space, Applied
Numerical Mathematics, 14 (1994), 199-211.
- R.E. Ewing,
R.D. Lazarov, and A.T. Vassilev,
Finite
difference scheme for parabolic problems on composite grids with refinement
in time and space, SIAM
J. Numer. Anal., 31(6) (1994), 1605-1622.
- R.E. Ewing,
R.D. Lazarov, and P.S. Vassilevski,
Local
refinement techniques for elliptic problems on cell-centered grids, II: Optimal
order two-grid iterative methods,
Numer.
Linear Algebra Appl., 1(4) (1994), 337-368.
- S.G. Carey,
R.D. Lazarov, and A.I. Pehlivanov, Least-squares mixed finite elements for second
order elliptic problems,
SIAM J. Numer. Anal., 31 (5) (1994), 1368-1377. MR#95i:65206.
- Z. Cai, R.D.
Lazarov, T.A. Manteuffel, and S.F. McCormick, First order systems least-squares
for partial differential equations: I. Discretization,
SIAM J. Numer. Anal., 31 (6) (1994), 1785-1799. MR# 95f:65133.
- S. Maliassov,
Yu.A. Kuznetsov, R.D. Lazarov, and R.E. Ewing,
Substructure
preconditioning for porous flow problems, Finite Element Modeling for
Environmental Problems, Chapter 17, John Wiley and Sons, New York, (1994),
303-329.
- P.S. Vassilevski,
S.I. Petrova, and R.D. Lazarov, Preconditioning elliptic problems on grids with
multilevel local refinemnet, Mathematica Balkanica, 8 (2-3)
(1994), 179-196.
-
R.D. Lazarov, I.D. Mishev, and P.S. Vassilevski,
Finite volume approximation of convection-diffusion problems on
grids with local refinement, Computing , 53 (1) (1994) 33-57.
- A. Andreev,
M. Apostolova, P. Binev, B. Boyanov, T. Boyanov, S. Dimova, D. Dryanov, A.
Iotova, G. Nikolov, R. Lazarov, M. Nikolcheva, M. Petkov, and T. Chernogorova,
Collection of Problems on Numerical Analysis, Sofia University Publ. House,
Sofia, 1994 (Bulgarian) .
1993
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- R.E. Ewing
and R.D. Lazarov,
Superconvergence of the mixed finite element approximations
of parabolic problems using rectangular finite elements, East-West
J. Numer. Math., 1(3) (1993), 199-212.
- A.I. Pehlivanov,
G.F. Carey, R.D. Lazarov, and Y. Shen, Convergence analysis of the least-square
mixed finite elements,
Computing , 51 (1993), 111-123. MR# 95b:65096.
- R.E. Ewing,
R.D. Lazarov, J.E. Pasciak, and P.S. Vassilevski, Domain decomposition type
iterative techniques for parabolic problems on locally refined grids,
SIAM J. Num.
Anal. 30(6) (1993), 1537-1557.
1992
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- A.I. Pehlivanov,
G.F. Carey, S.S. Show, and R.D. Lazarov, Superconvergence analysis of the approximate
boundary-flux calculations,
Numerische Mathematik, 63 (1992), 483-501.
- P.S. Vassilevski,
R.D. Lazarov, and S.I. Petrova, Finite difference schemes on triangular cell-centered
grids with local refinement,
SIAM J. Statistical and Scientific Computation, 13(6) (1992),
1287-1313.
- R.E. Ewing,
R.D. Lazarov, and A.T. Vassilev, Adaptive techniques for time-dependent problems,
Comp.
Meth. Appl. Mech. Engng. 101(3) (1992), 113-126.
1991
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- S.S. Chow, G.F.
Carey, and R.D. Lazarov, Natural and postprocessed superconvergence in semi-linear
problems,
Numer. Methods for Partial Diff. Equations, 7(4) (1991),
245-259.
- R.D. Lazarov
and A.I. Pehlivanov, Local superconvergence analysis of 3-D linear finite
elements for boundary flux-calculations, The Mathematics of Finite Elements
and Applications VII, MAFELAP 1990 (J.R.Whiteman ed.), Academic Press,
1991, 65-74 .
- R.E. Ewing,
R.D. Lazarov, and P.S. Vassilevski, Local refinement techniques for elliptic
problems on cell-centered grids. I: Error analysis,
Math.
Comp., 56(194) (1991), 437-462.
- R.E. Ewing,
R.D. Lazarov, and P.S. Vassilevski, Local refinement techniques for elliptic
problems on cell-centered grids. III: Algebraic multilevel BEPS preconditioners,
Numerische
Mathematik, 59 (1991), 431-452.
- R.E. Ewing,
R.D. Lazarov, and J. Wang, Superconvergence of the velocity along the Gauss
lines in the mixed finite element methods,
SIAM J. Numer. Anal., 28(4) (1991), 1015-1029.
- R.E. Ewing,
R.D. Lazarov, and P.S. Vassilevski, Finite difference schemes on grids with
local refinement in time and space for parabolic problems, II. Optimal order
two-grid iterative methods, Lecture Notes in Fluid Mechanics, Vieweg Publishers,
31 (1991), 70-93.
- R.E. Ewing,
R.D. Lazarov, and P.S. Vassilevski, Mixed finite element solutions of second
order elliptic problems on grids with regular local refinement, Domain
Decomposition Methods for Partial Differential Equations (R. Glowinski, Y.
Kuznetsov, G. Meurant, J. Periaux, and O. Widlund, Eds.), SIAM Publishers,
Philadelphia, PA, (1991), 206-212.
- V.M. Petkov and
R.D. Lazarov, Eds., Integral Equations and Inverse Problems, Pitman
Research Notes in Mathematics Series, 235 (1991), Longman Scientific & Technical,
285 p.
1990
Top
Home
- R.E. Ewing,
R.D. Lazarov, P. Lu, and P.S. Vassilevski, Preconditioning indefinite systems
arising from mixed finite element discretization of second-order elliptic
problems, Preconditioned Conjugate Gradient Methods (O. Axelsson and L.
Kolotilina, eds.), Lecture Notes in Mathematics, 1457 (1990) Springer-
Verlag, Berlin, 28-43.
- R.E. Ewing,
R.D. Lazarov, T.F. Russell, and P.S. Vassilevski, Local refinement via domain
decomposition techniques for mixed finite element methods with rectangular
Raviart-Thomas Elements, Domain Decomposition Methods for Partial Differential
Equations (T.F. Chan, R. Glowinski, J. Periaux, and O. Widlund, Eds.),
SIAM Publications, Philadelphia, Pennsylvania, (1990), 98-114.
- R.D. Lazarov,
Local superconvergence analysis of the approximate boundary-flux calculations.
Proc. of EQUADIFF'6 Conference, Teubner-texte zur Mathematik, 118
(1990) Leipzig, 275-278.
- R.E. Ewing,
R.D. Lazarov, and P.S. Vassilevski, Finite difference schemes on grids with
local refinement in time and space for parabolic problems, I. Derivation,
stability, and error analysis,
Computing 45 (1990) 193-215.
1989
Top
Home
- N. Andreev,
S. Dimova, R. Lazarov, V. Manolov, Tz. Rashev, and Bl. Sendov, Mathematical
modelling of some heat transfer processes in the steel casting industry, Proc.
of Int. Conf. on High Nitrogen Steels, Varna, 1989, 178-184.
- R.D. Lazarov
and V.G. Pasheva, Boundary element method for 2-D problems of ideal fluid flows
with free boundaries, Adv. Water Resources, 12 (1989), 37-45.
- S.S. Chow and
R.D. Lazarov, Superconvergence analysis of flux computations for nonlinear
two-point boundary value problems, Bull. Austr. Math. Soc., 40
(1989), 465-480, Zb#676.65096.
- R.E. Ewing
and R.D. Lazarov, Local refinement techniques in the finite element and finite
difference methods, Numerical Methods and Applications, Publishing
House of the Bulgarian Acad. Sci. , Sofia, Bulgaria, 1989, 148-159.
1988
Top
Home
- R.E. Ewing
and R.D. Lazarov, Adaptive local grid refinement, SPE No. 17806, Proceedings
of 1988 Rocky Mountain Regional Meeting of SPE, Casper, Wyoming, May 1988,
643-652; Proc. Fourth Wyoming Enhanced Oil Recovery Symposium,
Casper, Wyoming, (1988) 87-102.
- R.D. Lazarov,
Superconvergence of the gradient for triangular and tetrahedral finite elements
for solving linear problems of elasticity, Comput. Meth. and Systems,
Nauka, Moscow, 6 (1988) 143-153 (Russian), Zb#694.73023.
- A.B. Andreev
and R.D. Lazarov, Lumped mass finite element method for parabolic and eigenvalue
problems, Mathematika Balkanica, New Series, 2(1) (1988), 84-92,
Zb#000.65108.
- A.B. Andreev
and R.D. Lazarov, Superconvergence of the gradient for quadratic triangular
finite elements,
Numer. Methods for Partial Diff. Equations, 4(1)
(1988), 15-32, Zb#644.65082.
- K.N. Godev,
R.D. Lazarov, V.L. Makarov, and A.A. Samarskii, Homogeneous difference schemes
for one dimensional problems with generalized solutions, Math. USSR Sbornik,
59(1) (1988), 155-179, MR#88h:65145, Zb#621.65094.
- P.S. Vassilevski,
R.D.Lazarov, and S.D. Margenov, Solving elliptic problems by the domain decomposition
method using preconditioning matrices by multilevel splitting of the finite
element matrix, Lecture Notes in Computer Science, 297 (1988),
826-835, MR#89b:65270.
1987
Top
Home
- A.A. Samarskii,
R.D. Lazarov and V.L. Makarov, Difference Schemes for Differential Equations
Having Generalized Solutions, Visshaya Shkola Publ., Moscow, 1987,
296 pp.
- R.D. Lazarov
and P. Peykov, Modelling and investigation by simulation of semiconductor
pressure sensors, Bulg. J. Physics, 14(6) (1987), 530-541.
- K.N. Godev
and R.D. Lazarov, Truncated finite difference schemes for second boundary
value problems for ordinary differential equations, Proc. Conference on
Diff. Equations'85, Russe, Bulgaria, 1987, 675-682, MR#88k:65070.
1986
Top
Home
- V. Kantchev
and R.D. Lazarov, Superconvergence of the gradient of linear finite elements
for 3-D Poisson equation, Optimal Algorithms, Sofia, 1986, 172-182,
Zb#672.65088.
- N. Andreev,
I. Dimov, S.N. Dimova, R.D. Lazarov, V. Manolov, Bl. Sendov, Numerical simulation
of some technology problems in metallurgy, Math. Models Analytic and Numer.
Methods in Heat Transfer, 2 (1986), Acad. Sci. Belorus.SSR,
106-114.
- S.N. Dimova
and R.D. Lazarov, Study of some physical processes by means of the numerical
experiment, Summer School of Computer Applications in Science, Varna,
1986, 25-36.
1985
Top
Home
- S.N. Dimova,
A.I. Jotova and R.D. Lazarov, Finite element package TERMO for solving heat
problems, Numer. Meth. and Packages for Solving Problems of Math. Phys.,
Comput. Center Acad. Sci. USSR, Novosibirsk, 1985, 31-41.
- R.D. Lazarov
and P.I. Shopov, A package for solving Stokes equations using finite elements
with condensation, Proc. of Conf. on Numer. Meth. and Appl.'84, Sofia,
1985, 552-558.
- K.N. Godev
and R.D. Lazarov, Convergence of difference schemes for elliptic problems
with variable coefficients, Proc. Conf. on Numer. Meth. and Appl.'84,
Sofia, 1985, 308-313.
- A. Andreev,
B. Boyanov, S. Dimova, R. Lazarov, and M. Nikolcheva, Collection of Problems
on Numerical Analysis, Nauka i Izkustvo Publ. House, Sofia, 1985 (Bulgarian)
- K.N. Godev
and R.D. Lazarov, On the convergence of the difference scheme for the second
boundary value problem for the biharmonic equation with solution
from W^m,
Math. Models in Phys. Chem. and Numerical Methods of Their Realization,
Teubner-texte zur Math., 61 (1985), 130-141, MR#87b:65175, Zb
#542.65054.
1984
Top
Home
- S.N. Dimova,
N.T. Drenska, and R.D. Lazarov, Mathematical modelling of heat transfer in ingot
cristalization, Comput. Math., Banach Center Publ., 13 (1984),
73-90 (Russian).
- R.D. Lazarov,
V.L. Makarov, and W. Weinelt, On the convergence of difference schemes for
the approximation of solutions u from W^m (m>0.5) of elliptic equations with
mixed derivatives,
Numer.
Math., 44 (1984), 223-232, MR #86f:65181,Zb #525.65069.
- A.B. Andreev,
M.El Hatri, and R.D. Lazarov, Superconvergence of the gradient in the finite
element method for some elliptic and parabolic problems, Variational-Difference
Methods, Moscow, 1984, 13-25, Zb#605.65069.
- K.N. Godev
and R.D. Lazarov, Error estimates of finite difference schemes in L_p-metrics
for parabolic boundary value problems, Comptes Rend. l'Acad. Bulg. Sci.,
37 (1984), 565-568, Zb #567.65069, MR#86e:65137.
- R.D. Lazarov,
W. Weinelt, and U. Streit, On the convergence order of difference schemes
for weak solutions of the heat equation, Diff. Equations, 20(7)
(1984) (Russian), MR #86b:65105, Zb # 554. 65068.
1983
Top
Home
- N. Andreev,
I. Dimov, S. Dimova, R. Lazarov. V. Manolov, T. Rashev, Mathematical modelling
of crystalization of steel blocks, Trudy Inst. of Metallurgy, 14(1)
(1983), 93-102 (Bulgarian).
- R.D. Lazarov,
On the numerical solution of some axially-symmetric elastic problems by finite
difference method, Diff. Equations, 19(3) (1983), 500-507 (Russian),
MR #84f:65076, Zb#534.73066.
- R.D. Lazarov
and Yu.I. Mokin, On the computation of the logarithmic potential, Soviet
Math. Dokl., 28 (1983), 320-323, MR #86d:31008, Zb #567.65070.
- R.D. Lazarov,
V.L. Makarov, and W. Weinelt, On the convergence of difference schemes for
elliptic equations with mixed derivatives and generalized solutions, Diff.
Equations, 19(7) (1983), 838-843, MR #85a:65153, Zb #547.65069.
- I. Gavriliuk,
R.D. Lazarov, and V.L. Makarov, Error estimates for difference schemes for
the second boundary value problem of biharmonic equation with minimal requirements
of smoothness, Dop. Acad. Sci. Ukrain. SSR, ser. A, 2 (1983), 6-9,
MR #85j:65039 Zb #541.65063.
- R.D. Lazarov,
V.L. Makarov, and A.A. Samarskii, Application of exact difference schemes
to the construction and study of difference schemes for generalized solutions,
Math. USSR Sbornik, 45(4) (1983), 461-171, MR #84g:65137, Zb #512.65068.
- I. Gavriliuk,
R.D. Lazarov, V.L. Makarov, and S. Pirnazarov, Estimates of the rate of convergence
of difference schemes for fourth order elliptic equations, USSR J. Comput.
Math. and Math. Physics, 23(2) (1983), 64-70, MR #85g:65115, Zb#541.65064.
1982
Top
Home
- R.D. Lazarov
and V.L. Makarov, Difference schemes of second order accuracy for the axially
symmetric Poisson equation on generalized solutions, Soviet Math. Dokl.,
25 (1982), 15-19, MR #83h:65114, Zb#488.65041.
- S.N. Dimova
and R.D. Lazarov, Numerical methods for some heat problems, Cisl. Modeli,
Analit. i Cisl. Metodi v Teorii Perenosa, (A.Samarskii, Ed.), Minsk,
ITMO (1982), 55-73.
- R.D. Lazarov,
On the convergence of the finite difference schemes for Poisson equation in
discrete H^1-norms, p=2, Wiss. Beitr. IH Wismar, 7 (1982), 86-90.
- R.D. Lazarov,
Error estimates of the finite difference schemes for parabolic problems on
generalized solutions, Comptes Rend. l'Acad. Bulg. Sci., 35(1)
(1982), 7-10 (Russian), MR #84a:65081 Zb #524.65067.
- R.D. Lazarov,
Convergence of difference method for parabolic equations with generalized
solutions, Pliska, 5 (1982), 51-59 (Russian), MR #84m:65105,
Zb #563.65063.
1981
Top
Home
- N. Andreev,
I. Dimov, S. Dimova, R. Lazarov. V. Manolov, T. Rashev, Mathematical modelling
of heat conduction in ingot casting of stainless steel, Metallurgy,
36 (1981),3-5.
- K.T. Georgiev
and R.D. Lazarov, An error estimate for the decomposed finite element solution
of the polyharmonic equation, Mathematics - Revue d'Analyse Numerique et
de Theorie d'Approximation, 23 (1981), 31-34, MR#83g:65106, Zb
#477.57015.
- R.D. Lazarov,
On the convergence of the difference schemes for Poisson equation with generalized
solutions, Diff. Equations, 17 (7) (1981), 829-836, MR #83f:65169,
Zb #485.65067.
- R.D. Lazarov,
Convergence of finite difference schemes on generalized solutions of the biharmonic
equation on a rectangle, Diff. Equations, 17 (7) (1981), 836-842,
MR #83h:65116, Zb #485.65068.
- R.D. Lazarov,
Error estimate for the finite difference schemes for generalized solutions
of the first boundary value axially symmetric elastic problems, Methods
of Appr. and Interpolation, (Yu. Kuznetsov, Ed.), Acad. Sci. of USSR,
Novosibirsk, 1981, 89-101, MR#87b:65175.
- P.G. Gospodinov,
R.D. Lazarov, and S.P. Radev, Numerical treatment of some problems of fluid
flow and instability of liquid jets, Meth. und Verfahren der Math. Physik,
Proc. Conf. on Math. in Fluid Mechanics, Obervolfach (1981), Zb #562.76042.
- R.D. Lazarov
and V.L. Makarov, Convergence of the difference methods and the methods of
lines for multidimensional problems in classes of generalized solutions, Soviet
Math. Dokl., 23 (1981), 69-73, MR #83a:35004, Zb #485.65069.
- R.D. Lazarov,
On the convergence of the difference schemes for some axisymmetric problems
of mathematical physics in classes of generalized solutions, Soviet Math.
Dokl., 23 (1981), 667-670 MR#83h: 65115, Zb #524.65065.
- R.D. Lazarov
and V.L. Makarov, Difference schemes of second order of accuracy for the axisymmetric
Poisson equation with generalized solutions, USSR J. Comput. Math. and
Math. Phys, 21(5) (1981), 95-107, MR #84b:65100, Zb #485.65066.
- R.D. Lazarov
and Yu.I. Mokin, On the convergence of the difference schemes for Poisson
equation in L_p-metrics, Soviet Math. Dokl., 24 (1981), 590-594,
MR #83d:65272, Zb #524.65066.
1980
Top
Home
- R.D. Lazarov
and E.A. Varbanova,
Difference schemes for 1-D coupled dynamic problems of thermoelasticity,
Ann. VUZ, Appl. Math., 16 (4) (1980), 167-178, (Russian), MR
# 83d:73080a, Zb# 497.73004.
- R.D. Lazarov,
On the convergence of the difference schemes for axially symmetric problems
of elasticity, Comm. JINR, Dubna, P11-80-884 (1980), 1-22 (Russian).
- N. Andreev,
I. Dimov, S. Dimova, R. Lazarov. V. Manolov, and T. Rashev, Mathematical
models of cristalization of block of nitrogen steel, casted in cylindrical
forms, Material Sci. and Technology, 9 (1980), 63-68 (Bulgarian).
- R.D. Lazarov
and E.A. Varbanova, Numerical solution of a coupled problem of elasticity, Ann.
VUZ, Appl. Math., 16(4) (1980), 179-191 (Bulgarian), MR # 83d:73080b,
Zb# 497.73005.
- R.D. Lazarov
and E.A. Varbanova, Self similar solutions of the coupled thermoelasticity,
Comm. JINR, Dubna, P5-80-886 (1980) (Russian).
1979
Top
Home
- R.D. Lazarov,
Factorized finite difference schemes of second order accuracy for solving
dynamic problems of elasticity, Comptes Rend. de l'Acad. Bulg. Sci.,
32 (1979), 1, 7-10 (Russian), Zb # 432.73079 MR# 80f:65133.
- K. Ganev and
R.D. Lazarov, An application of the splitting method for solving some problems
of mesometeorology, Bulgarian Geophysical J., 5 (1979), 11-21
(Russian).
- R.D. Lazarov
and G. Meladze, Factorized schemes for the dynamic problems of elastic vibrations
of an unbounded strip, Trudy Tbilissi State University, 207
(1979), 14-26 (Russian), Zb # 462.73038.
- M.S. Kaschiev
and R.D. Lazarov, Numerical solution of the two-dimensional Schrodinger equation
corresponding to a two-center problem, Comm. JINR, Dubna, P11-12307
(1979).
- R.D. Lazarov
and S.D. Margenov, An application of parabolic and cubic splines to solution
of fourth order elliptic boundary value problems on a rectangle, Preprint
N 64, Seminar on Methods of Comput. and Appl. Mathematics, Siberian Branch
Acad. Sci. of USSR, 1979 (Russian).
1978
Top
Home
- R.D. Lazarov,
V. Liubenov, and S. Pasheva, Problems with free lines, Proc. National School
of Young Scientists, VMEI, Sofia, 1978, pp. 53--63.
1977
Top
Home
- R.D. Lazarov,
Numerical methods for the problems of physics, mechanics and technique using
computers, Rutherford Laboratory, Didcot, UK, Final Report, 1977.
1976
Top
Home
- R.D. Lazarov
and P. Panayotov, Solving an axially-symmetric elastic problem by projection
difference method, Ann. VUZ, Applied Mathematics, 12 (2) (1976)
(Bulgarian), Zb# 432.73080.
- P.G. Gospodinov,
G. Saev, and R.D. Lazarov, Computing transient temperature fields by the finite
element method, Mashinostroenie, 1 (1976), 23-26 (Bulgarian).
- R.D. Lazarov
and L.G. Stoyanov, Difference schemes for mixed boundary value problems of elasticity
on triangular grids, Comm. VMEI Gabrovo, 8 (1976), 53-62 (Bulgarian).
- R.D. Lazarov,
Difference schemes of second order accuracy for the axisymmetric problems
of elasticity in a cylinder, Comptes Rend. de l'Acad. Bulg. Sci.,
29 (1976), 21-24 (Russian), Zb# 366.73011.
- R.D. Lazarov
and V.M. Petkov, Economical difference scheme for a mixed boundary value problem
of Neuman type for hyperbolic equations of second order, Math. and Math.
Education, Proc. Third Conf. Union Bulgarian Mathematicians, 1976, 209-215
(Bulgarian), Zb # 355.65075.
- R.D. Lazarov
and E.A. Varbanova Difference scheme for a mixed elastic problem in an orthotropic
cylinder, Proc. Sec. Nat. Congress Theoretical and Appl. Mech., Varna,
2 (1976), 235-243 (Russian).
- R.D. Lazarov
and G. Meladze, On the application of difference schemes for solving the problem
of a vibrating elastic strip, Bull. Acad. Sci. Georgian SSR, 83
(1976), 17-21 (Russian).
1975
Top
Home
- R.D. Lazarov,
E.P. Zhidkov, M.S. Kaschiev, Computing three-dimensional electrostatic fields
for rectangular electrodes, Comm. JINR, Dubna, 9-9181 (1975) (Russian).
- Chr. Butzev,
A.H. Hachikian, and R.D. Lazarov, On calculation of axially-symmetric electric
fields, Ann. Ecole Superieur de Mines et de Geologie, 21 (1)
(1975), 133-140 (Bulgarian).
- R.D. Lazarov,
Difference schemes for solving problems of elastic equilibrium of isotropic
cylinder, Cisl. Analys, Inst. of Cybern. of Ukrain. Acad. of Sciences,
1975, 3-19 (Russian).
- R.D. Lazarov,
Some methods of discretization of problems of mathematical physics, Proc.
National School on Application of Computers in Engineering, Primorsko,
1975, 195-208 Bulgarian)
- R.D. Lazarov,
A factorized scheme for an axially-symmetric dynamic problem of elasticity,
Ann. VIZ, Appl. Mathematics, 11 (2) (1975), 103-112 (Russian),
Zb# 395.73076.
- R.D. Lazarov
and M.S. Kaschiev, Numerical solution to some 3-D electrostatic problems,
modelling accelerating cameras, Math. and Math. Education, Proc. Fourth
Conf. Union Bulgarian Mathematicians, 1975, 221-226 (Bulgarian).
1974
Top
Home
- R.D. Lazarov
and E.A. Varbanova, Numerical solution to mixed boundary value problems of elasticity
in orthotropic cylinders, Ann. VUZ, Appl. Math., 10 (4) (1974), XXX
(Bulgarian), Zb# 343.73011.
1973
Top
Home
- R.D. Lazarov,
Difference schemes for problems of elasticity in domains with curvilinear
boundaries. II. Error estimate. Numerical experiments, Theoretical and
Appl. Mech., 4 (2) (1973), 133-124 (Russian).
- R.D. Lazarov,
Difference methods and their application to the problems of elasticity,
Math. and Math. Education, Proc. Second Conf. Union Bulgarian Math., 1973,
143-150 (Russian), Zb # 366.73011.
- R.D. Lazarov
and Yu.I. Mokin, On the stability of elliptic difference schemes, USSR
J. Comput. Math. and Math. Physics, 13 (2) (1973), 282-291 (Russian),
Zb # 432.73079.
- R.D. Lazarov
and Yu.I. Mokin, Stability of elliptic difference schemes in Lp-metrics,
Issl. Teorii Raznostn. Schem Ellipt. Parabol. Uravn., Moscow State Univ. Publishers
(1973), 40-88 (Russian).
1972
Top
Home
- R.D. Lazarov,
Difference schemes for problems of elasticity in domains with curvilinear
boundaries. I. Construction of the difference scheme. A priori estimate, Theoretical
and Appl. Mech., 2 (4) (1972), 19-30 (Russian).
1971
Top
Home
- R.D. Lazarov,
Difference schemes for the second boundary value problem of elasticity for
domains with curved boundaries, USSR J. Comp. Math. and Math. Physics,
11(4) (1971), 166-179.
- R.D. Lazarov,
Variational-difference schemes for axisymmetric problems of elasticity, Seminar
Inst. Appl. Math., Georgian State Univ., 5 (1971), 77-83
(Russian).
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Please send comments, questions, and requests for reprints to lazarov@math.tamu.edu