Jean-Luc Guermond
Professor, Exxon Mobil Chair

Education

• Habilitation Dissertation, Mathematics, University of Paris VI, France, 1995

• French Aggregation, Mathematics, University of Paris VI, France, 1990

• Ph.D, Theoretical Mechanics, University of Paris VI, France, 1985

• M.S., Theoretical Mechanics, University of Paris VI, France, 1983

In the Profession

• 2004-present, Professor, Department of Mathematics, Texas A&M

• 2001-2003, Visiting professor, ICES, UT Austin, TX

• 1990-2001, CNRS Research Scientist at LIMSI, Orsay, France

• 1987-1990, Research Associate at Bassin d'Essais de Carenes, Paris, France

• 1986-1987, Post-Doc, Department of Ocean Engineering, MIT, Boston, MA

• 1984-1986, Research Associate at Bassin d'Essais de Carenes, Paris, France

Research or Scholarly Interests

• Numerical Analysis: Finite element approximation, Discontinuous Galerkin methods, Stabilization, Multi-scale approximations, Homogenization.

• Partial Differential Equations: Navier-Stokes equations (From smoothness questions in 3D to Approximation), Magneto-hydodynamics, Maxwell equations, Transport equations, Conservation laws, Hamilton-Jacobi equations.

Major Awards and Invitations

• (02-2019 to 01-2023) International INRIA Chair
  

• 05-06/2015 (one month), CERMICS, ENPC, France.

• 06-07/2015 (one month), Invited professor, University Paris XI, FR.

• 01-2015, (three weeks) Invited professor, University Paris XI, FR.

• 07/2014, (one month) Invited professor, Aix-Marseille University, FR.

• 01, 05/2014 (two months) Invited professor, University Paris XI, FR.

• 04-05/2013 (two months) Invited professor, University Paris Est, FR.

• 01-02/2013, (one month) Invited professor, University Paris XI, FR.

• 10/2012-, Exxon Mobile Chair.

• 06-07/2012, (one month) Invited professor, University Paris XI, FR.

• 05-06/2012, (one month) Invited professor, University Nice, FR.

• 20-24/08/2012, (one week) CERMICS, ENPC, France.

• 01-02/2011, (one month) Invited professor, University Paris XI, FR.

• 05/2011, (one month) Invited professor, CERMICS, Ecole Nationale des Ponts et Chaussees, Marnes La vallee, FR.

• 01-02/2011, (one month) Invited professor, University Paris XI, FR.

• 04/2010, (one month) Invited professor, university Nice, FR.

• 01/2010, (one month) Invited professor, University Paris XI, FR.

• 06/2009, (one month) Invited professor, University Paris XI, FR.

• 04/2009, (one month) Invited professor, Nice University, FR.

• 06/2008, (one month) Invited professor, University Paris XI, FR.

• 06/2006, (one month) Invited professor, University Paris XI, FR.

• 07/2005, (two weeks) Invited professor, Ecole Nationale des Ponts et Chaussees, FR..

• 01-02/2004, (one month) Invited professor at the University of Purdue, Indiana, IN.

• 08/2002 to 07/2003, TICAM fellowship, Austin, TX.

• 08/2002, (one month) Invited professor at the University of Edmonton, Canada.

Notable Recent Grants

• AFOSR (FA9550-18-1-0397 PI,  (Aug 2018-Aug 2021)
  

• ARO (W911NF-15-1-0517) PI, Aug 2015, July 2017, Finite Element Approximation Of Nonlinear-Systems Developing Shocks Fronts And Interfaces

• AFOSR (FA9550-15-1-0257), PI, July 2015, Sept 2017, Robust Approximation Of Nonlinear Hyperbolic Systems

• AFOSR (FA9550-12-1-0358), PI, July 2012-April 2015, High-order approximation techniques for nonlinear hyperbolic PDEs, PI.

• NSF (DMS - 1217262), Co-PI, August 2012-July 2015, Entropy viscosity and L1-based approximation of PDEs: Exploring Sparsity, co-PI.

• IAMCS Innovation grant, August 2010-May 201, PI.

• AFOSR, L1-Based approximations for PDEs and Applications, PI, April 2009-April 2011.

• US DOE (C09-00035) 09 Sep 2008 to 30 June 2011, ``Support of Stockpile Stewardship Program'', Co-PI.

• NSF-DMS (0811041), July 2008 to June 2011, ``L1-based Approximation Techniques for PDEs'', Co-PI.

• NSF-DMS (0713829), Aug 2007 to Aug 2010, ``Discontinuous Galerkin Methods for PDEs with Heterogeneous Coefficients'', PI.

• US DOE (C08-00358), Sept 07 to Sept 08, ``High Fidelity 3-D Core Model for Light Water Reactor Nuclear Reactors'', Co-PI.

• NSF-DOE (07-545), ``Framework for Developing Novel Detection Systems Focused on Interdicting Shielded HEU'', Co-PI.

• NFS-DMS (0510650), June 2005 to May 2008, "Nonlinear finite element approximation of first-order PDE's in L1", PI.

• NFS, DGE - IGERT (0523626):  (2005-2010) "IGERT: New Mathematical Tools for Next Generation Materials", Co-PI.

Recent Publications or Scholarly Works (2013-present)

J.-L.GUERMOND, B. POPOV, IGNACIO TOMAS, Invariant domain preserving discretization-independent schemes and convex limiting for hyperbolic systems, Comput. Methods Applied Mech. Engin., 347 (2019) 143–175. (Reprint).

J.-L.GUERMOND, B. POPOV, LAURA SAAVEDRA, YONG YANG, Arbitrary Lagrangian-Eulerian Finite Element Method Preserving Convex Invariants of Hyperbolic Systems, in Contributions to Partial Differential Equations and Applications, Chetverushkin, B. N., Fitzgibbon, W., Kuznetsov, Y.A., Neittaanmaki, P., Periaux, J., Pironneau, O., Eds., Springer International Publishing, (2019) 251--272, (Reprint).

J.-L.GUERMOND, M. QUEZADA de LUNA, B. POPOV, C. KEES, M. FARTHING, Well-balanced second-order finite element approximation of the shallow water equations with friction, SIAM, J. Sci. Comput., 40:6 (2018) A3873—A3901. (Reprint).

J.-L.GUERMOND, M. NAZAROV, B. POPOV, I. TOMAS, Second-order invariant domain preserving approximation of the Euler equations using convex limiting, (supplementary), SIAM J. Sci. Comput., 40  5 (2018) A3211--A3239, (Reprint) and (supplemetary material),

C. NORE,  D. CASTANON QUIROZ, LOIC CAPPANERA, J.-L. GUERMOND, Numerical simulation of the Von-Karman-Sodium dynamo experiment, J. Fluid Mech., 854 (2018) 10 November 2018, 164--195, (Reprint),

R. ZANELLA, C. NORE, F. BOUILLAULT, J-L.GUERMOND, X. MININGER, Influence of thermomagnetic convection and ferrofluid thermophysical properties on heat transfers in a cylindrical container heated by a solenoid, Journal of Magnetism and Magnetic Materials, 429 (2018) 52–63, (Reprint).

A. ERN, J.-L. GUERMOND, Analysis of the edge finite element approximation of the Maxwell equations with low regularity solutions, Computers and Mathematics with Applications, https://doi.org/10.1016/j.camwa.2017.10.017, (2018) 1--15 (Reprint).

L. CAPPANERA, J.-L. GUERMOND, W. HERREMAN, C. NORE, Momentum-based approximation of incompressible multiphase fluid flows, Int. J. Numer. Fluids, 86 (2018) 541--563, DOI: 10.1002/fld.4467, (Reprint).

RAPHAEL ZANELLA, CAROLINE NORE, FREDERIC BOUILLAUT, LOIC CAPPANERA, IGNACIO TOMAS, XAVIER MINIGER, and JEAN-LUC GUERMOND, Study of Magnetoconvection Impact on a Coil Cooling by Ferrofluid with a Spectral/Finite-Element Method, IEEE Transactions on Magnetics, 54:3 460014, DOI: 10.1109/TMAG.2017.2749539, (Reprint).

P. AZERAD, J.-L. GUERMOND, B. POPOV, Well-balanced second-order approximation  of the shallow water equation with continuous finite elements, SIAM J. Numer. Anal. 55:6 (2017)  3203--3224 (Reprint).

J.-L.GUERMOND, B. POPOV, Invariant domains and second-order continuous finite element approximation for scalar conservation equations,  SIAM J. Numer. Anal. 55 6 (2017) 3120-3146, (Reprint)

A. ERN, J.-L. GUERMOND, Abstract Nonconforming Error Estimates and Application to Boundary Penalty Methods for Diffusion Equations and Time-Harmonic Maxwell’s Equations, Comput. Methods Appl. Math., https://doi.org/10.1515/cmam-2017-0058, (2017) 1--25 (Reprint).

L. CAPPANERA, J.-L. GUERMOND, W. HERREMAN, C. NORE, Momentum-based approximation of incompressible multiphase fluid flows, Int. J. Numer. Fluids, DOI: 10.1002/fld.4467, (2017) (Reprint)

RAPHAEL ZANELLA*, CAROLINE NORE, FREDERIC BOUILLAUT, LOIC CAPPANERA*, IGNACIO TOMAS*, XAVIER MINIGER, and JEAN-LUC GUERMOND, Study of Magnetoconvection Impact on a Coil Cooling by Ferrofluid with a Spectral/Finite-Element Method, IEEE Transactions on Magnetics, DOI: 10.1109/TMAG.2017.2749539, (Reprint).

A. ERN, J.-L. GUERMOND, Finite element quasi-interpolation and best approximation, Math. Mod. Numer. Anal., M2AN, 51 4 (2016) 1367--1385 (Reprint).

J.-L.GUERMOND, M. QUEZADA de LUNA, T. THOMPSON, A conservative anti-diffusion technique for the level set method, J. Comput. Appl. Math., 321 (2017) 448–468, (Reprint).

J.-L.GUERMOND, B. POPOV, LAURA SAAVEDRA, YONG YANG*, Invariant domains preserving Arbitrary Lagrangian Eulerian approximation of hyperbolic systems with continuous finite elements, SIAM J. Sci. Comput., 39 2 (2017) A385--A414, (Reprint).

J.-L.GUERMOND, B. POPOV, YONG YANG*, The Effect of the Consistent Mass Matrix on the Maximum-Principle for Scalar Conservation Equations, Journal of Scientific Computing, 70 (3) (2017) 1358--1366, (Reprint).


J.-L.GUERMOND, P. MINEV, High-order time stepping for the Navier-Stokes equations with minimal computational complexity, Journal of Computational and Applied Mathematics, 310 (2017) 92--103 (Reprint) (Arxiv).

A. BONITO, J.-L.GUERMOND, F. LUDDENS, An Interior Penalty Method with C0 Finite Elements for the Approximation of the Maxwell Equations in Heterogeneous Media: Convergence Analysis with Minimal Regularity, Math. Modelling and Numer. Anal. (M2AN) (2016) http://dx.doi.org/10.1051/m2an/2015086

A. ERN, J.-L. GUERMOND, Mollification in strongly Lipschitz domains with application to continuous and discrete De Rham complex, Computational Methods in Applied Mathematics,Volume 16, Issue 1, (2016) 51—75. (Reprint)

J.-L. GUERMOND, B. POPOV, V. TOMOV, Entropy–viscosity method for the single material Euler equations in Lagrangian frame, Computer Methods in Appl. Math. And Engin., 300 (2016) 402—426. (Reprint)

J.-L. GUERMOND, B. POPOV, Error estimates of a first-order Lagrange finite element technique for nonlinear scalar conservation equations, SIAM J. Numer. Anal., 54:1 (2016) 57—85. (Reprint)

A. BONITO, J.-L. GUERMOND, S. LEE, Simulations of bouncing jets, Int. J. Numer. Methods Fluids, 80 (2016) 53—75. (Reprint)

H. ZAIDI, F. BOUILLAUT, C. NORE, A. BOSSAVIT, J.-L. GUERMOND, Approximation of the time-dependent induction equation with advection using Whitney elements: application to dynamo action, COMPEL – The international journal for computation and mathematics in electrical and electronic engineering 35:1, (2016) 326—338. (Reprint)

J.-L.GUERMOND, P. MINEV, High-order Time Stepping for the Incompressible Navier-Stokes equations, SIAM J. Sci. Comput.,37(6) (2015) A2656—A2681. (Reprint)

W. HERREMAN, C. NORE, L. CAPPANERA, J.-L. GUERMOND, Tayler instability in liquid metal columns and liquid metal batteries, Journal of Fluid Mechanics, 771 (2015) 79—114, (Reprint)

C. NORE, D. CASTANON QUIROZ, J.-L. GUERMOND, J. LEORAT, and F. LUDDENS, Numerical dynamo action in cylindrical containers, Eur. Phys. J. Appl. Phys. (2015) 70:31101, (Reprint)

A. BONITO, J.-L. GUERMOND, S. LEE, Simulations of bouncing jets, Int. J. Numer. Methods Fluids, (Reprint).

A. RIBEIRO, G. FABRE, J.-L. GUERMOND, J. AURNOU, Canonical Models of Geophysical and Astrophysical Flows:Turbulent Convection Experiments in Liquid, Metals (2015), 5, 289-335. (Reprint)

J.-L. GUERMOND, A. LARIOS, T. THOMPSON, Validation of an entropy-viscosity model for large eddy simulation, Direct and Large Eddy-Eddy Simulation IX, ECOFTAC Series Volume 20, (2015) 43-48. (Reprint)

C. NORE, J. LEORAT, J.-L.GUERMOND, A. GIESECKE, Mean-field model of the von Kármán sodium dynamo experiment using soft iron impellers, Physical Review E, 91 013008  (2015) 1-12 (Reprint)

R. PASQUETTI, J.-L. GUERMOND, B. POPOV, Stabilized spectral element approximation of the Saint Venant system using the entropy viscosity technique, Int. Conf. on Spectral and High Order Methods (ICOSAHOM 2014), Lecture Notes in Computational Science and Engineering, Vol. 106 Springer International Publishing, (2015) 397—404. (Reprint)

J.-L. GUERMOND, M. NAZAROV, B. POPOV,Y. YANG, A second-order maximum principle preserving Lagrange finite element technique for nonlinear scalar conservation equations, SIAM, J. Numer. Anal., 52:4 (2014) 2163—2182.

J.-L.GUERMOND, B. POPOV, Viscous regularization of the Euler equations and entropy principles, SIAM J. Appl. Math., 74 2 (2014) 284-305.

J.-L.GUERMOND, M.NAZAROV, A maximum-principle preserving C0 finite element method for scalar conservation equations, Computer Methods in Appl. Math. and Engin., 272 (2014) 198–213.

P. MARTI, N. SCHAEFFER, R. HOLLERBACH, D. CEBRON, C. NORE, F. LUDDEENS, J.-L. GUERMOND, J. AUBERT, S. TAKEHIRO, Y. SASAKI, Y.-Y. HAYASHI, R. SIMITEV, F. BUSSE, S. VANTIEGHEM, A. JACKSON, Full sphere hydrodynamic and dynamo benchmarks, Geophysical Journal International, 197 (2014), 119-134.

A. JACKSON, A. SHEYKO, P. MARTI, A. TILGNER, D. CEBRON, S. VANTIEGHEM, R. SIMITEV, F. BUSSE, X. ZHAN, G. SCHUBERT, S. TAKEHIRO, Y. SASAKI, Y.-Y. HAYASHI, A. RIBEIRO, C. NORE, and J.-L. GUERMOND, A spherical shell numerical dynamo benchmark with pseudo-vacuum magnetic boundary conditions, Geophysical Journal International, 196 (2014) 712-723.

A. BONITO, J.-L. GUERMOND, B. POPOV, Stability Analysis of the Explicit Entropy Viscosity Method for Scalar Non-Linear Conservation Laws, Mathematics of Computation, 83 287 (2014) 1039-1062.

J.-L. GUERMOND, G. KANSCHAT, J.C. RAGUSA, Discontinuous Galerkin methods for the radiative transport equation, in Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations 2012 John H Barrett Memorial Lectures Series, The IMA Volumes in Mathematics and its Applications, Vol. 157, Vol. 157, Feng, Xiaobing; Karakashian, Ohannes; Xing, Yulong (Eds.), Springer (2014), 181-193.

J.-L. GUERMOND, B. POPOV, Entropy viscosity for the Euler equations and questions regarding parabolic regularization, Hyperbolic Problems: Theory, Numerics, Applications, Proceedings of HYP2012, American Institute of Mathematical Sciences, Vol. 8 (2014) 119-124.

A. BONITO, J.-L. GUERMOND, B. POPOV, Stability Analysis of the Explicit Entropy Viscosity Method for Scalar Non-Linear Conservation Laws, Mathematics of Computation (2013), S 0025-5718(2013)02771-8, Article electronically published on October 3, 2013.

A. BONITO, J.-L. GUERMOND, F. LUDDENS, Regularity of the Maxwell equations in heterogeneous media and Lipschitz domains, J. Math. Anal. Appl., 408 (2013) 498–512.

T. GORNAK, J.-.L. GUERMOND, O. ILIEV, P. MINEV, A Direction Splitting Approach For Incompressible Brinkman Flow, International J. Numer. Anal. Modelling, Series B, 4:1 (2013) 1-13.

A. ERN, J.-.L. GUERMOND, Weighting the edge stabilization, SIAM J. Numer. Anal., 51:3 (2013) 1655-1677.

J.-.L. GUERMOND, J. LEORAT, F. LUDDENS, C. NORE, Remarks on the stability of the Navier-Stokes equations supplemented with stress boundary conditions, European Journal of MechanicsB/Fluids, 39 (2013) 1-10.

V. ZINGAN, J.-.L. GUERMOND, J. MOREL, B. POPOV, Implementation of the entropy viscosity method with the Discontinuous Galerkin Method, Compter. Methods in Appl. Math. and Engin.,  253 (2013) 479-490.

J.-.L. GUERMOND, R. PASQUETTI, A correction technique for the dispersive effects of mass lumping for transport problems, Compter. Methods in Appl. Math. and Engin., 253 (2013)  186-198.

Recent Synergistic Activities

• Editorial activities: associate editor for JMAA, IJNA, (SIAM SISC 2012-2015)

• University activities:Committee of Principal Investigators (TAMU): 2009-2012; 2012-2015; Faculty-Student IP Agreement Task Force: 2014-2015; Evaluation Committee of TOP grants 2012, 2014, 2015; Task Force for Faculty Performance Evaluations: 2009/2010.

• Departmental activities: Coordinator of the Numerical Analysis seminar 2005-2008; Post-Doc Committee: 2004-205, 2012-2013; Undergraduate Committee: 2011-2012; IUMRI Search Committee: 2011; Head Search Committee: 2010; Award Committee: 2009-2011; Committee P (Promotion): 2005-2007, 2014-2016 chair in 2006/2007 and 2015/2016; Executive Committee: 2005-2007;

Recent Graduate Students and/or Postdocs

• Postdoc mentored prior to 2005: 1
  

• Postdocs mentored since 2005: 6
  

1. Francois Marpeau, Post-Doc, Texas A&M, (2005-2006).

2. Vesselin Dobrev, Post-Doc, Texas A&M, (2007-2009).

3. Adam Larios, Post-Doc, Texas A&M, (2011-2014)

4. Murtazo Nazarov, Post-Doc, Texas A&M, (2011-2014)

5. Aziz Takirov, Post-Doc, Texas A&M (2014-2017)

6. Ignacio Tomas, Post-Doc, Texas A&M (2015-2018)

• Phd Students prior to 2003: 7
  

• Phd Students since 2003: 13

1. Raphael Laguerre, Univ. Paris VII; 2003-2006; Co-chair.

2. Adolfo Ribeiro, Univ. Paris XI; 2006-2010; Co-chair.

3. Abner Salgado, Texas A&M; 2006-2010; Chair

4. Valentin Zingan; Nuclear Engineering; 2009-Spring 2012; Co-Chair.

5. Franky Luddens; Univ. Paris XI; 2009-Fall 2012; Co-chair.

6. Habiballah Talavatifard; Texas A&M; 2010-Spring 2013; Chair. (Defended a MS Thesis)
   

7. Travis Thomson; Texas A&M; Fall 2011-2013; Chair
   

8. Daniel Castanon Quiroz; Texas A&M, Spring 2012-Spring 2015; Chair
   

9. Fahad Alrashed; Texas A&M, Fall 2011- Spring 2015; Aramco support; Chair
   

10. Loic Cappanera; Paris XI, France; Fall 2012-Fall 2015; Co-chair.

11. Daniel Castanon ; Texas A&M ; Falll 2011-(spring 2016); Chair.

12. Yong Yang, Texas A&M, Fall 2012-(Spring 2016); Chair

13. Manuel Quezada, Texas A&M, Fall 2012-(Spring 2016); Chair.

14. Raphael Zanella, Paris XI, France; Fall 2015-(Fall 2018); Co-chair.