Instructor: Prof. Jean-Luc Guermond,
507C Blocker
Office Hours: TR,
12:50-14:00 and 17:20-18:30
Class Times: 14:20-15:35, TR
Bloc 160
Advanced material
on the finite element methods for solving partial differential
equations; stability, consistency,
convergence of methods and
error bounds.
Interpolation theory of Finite Elements : Scalar-valued (Lagrange, modal) and vector valued (Raviart-Thomas, Nedelec)
Quasi-interpolation
Inverse Inequalities
Elementary functional analysis for linear PDE's (Closed Range Theorem, Open Mapping, BNB Theorem, inf-sup conditions)
Galerkin approximation.
Approximation of some elliptic PDE's (Galerkin, Crouzeix-Raviart, Discontinuous Galerkin, Interior Penalty)
Saddle point problems (Darcy, Maxwell, Stokes)
First-order PDEs and stabilization
Eigenvalue problems
Time-dependent PDEs (Heat, Stokes)
Nonlinear scalar conservation equations
Lectures notes will
be made available for each class on the web site.
Most of the material will come from:
Theory
and Practice of Finite Elements (Applied Mathematical Sciences)
Alexandre Ern & Jean-Luc Guermond,
Springer
Verlag
Two midterm exams and one final exam:
Flipped classes (Sept 14, 19, and 21).
Flipped classes (Oct 24, Oct 26 and Oct 31).
Final: There will be a final oral exam on Dec 5th in Bloc 160
Grading Policy:
33% will be determined by the two midterm and 34% by the final exam.
Your MINIMUM grade will be A, B, C, or D, for averages of 90%, 75%, 65%, or 45%, respectively.
Students must make arrangements in advance if they expect
to miss an exam.
Exam absences due to recognized
University-related activities, religious holidays,
verifiable
illness, and family/medical emergencies will be dealt with on an
individual basis.
In all cases of absence from exams a written
excuse is required.
Ignorance of the time and place of an exam
will not be accepted as an excuse for absence.
Students with
disabilities and special needs are referred to the office of support
services.
The office will then notify me about the details and
special arrangements that should be made.
If you believe you
have a disability requiring an accommodation,
please contact
Disability Services, in Cain Hall, Room B118, or call 845-1637.
More
information about Disability
Services can be obtained from their website.
Dean of Faculties:http://dof.tamu.edu/
Center for Teaching Excellence:http://cte.tamu.edu/
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Aggie Honor System Office:http://aggiehonor.tamu.edu/
Student Learning Outcomes and Catalogs:http://catalog.tamu.edu/