Content
Course Description:
This course is an introduction to the theoretical and computational aspects of the finite element method for the solution of boundary value problems for partial differential equations. Emphasis will be on linear elliptic, selfadjoint, secondorder problems, and some material will cover time dependent problems as well as nonlinear problems. Topics include: Sobolev spaces, variational formulation of boundary value problems, natural and essential boundary conditions, LaxMilgram lemma, approximation theory, error estimates, element construction, continuous, discontinuous, and mixed finite element methods, and solution methods for the resulting finite element systems.
Tentative Syllabus:
 FEM for two point boundary value problems
 Brief introduction to Sobolev Spaces
 FEM for elliptic equations
 Approximation theory for FEM
 FEM for parabolic equations
Textbook:
The course will not follow closely a specific textbook. Here are some recommended references.

The mathematical theory of finite element methods. S.C. Brenner and L.R. Scott, SpringerVerlag 1994.

Numerical analysis of partial differential equations. C. Hall and T. Porsching, 1990.

Understanding and implementing the finite element method. M. Gockenbach, SIAM 2006.

Finite elements: Theory, fast solvers, and applications in solid mechanics, 3rd ed. D.Braess, Cambridge 2007.

The finite element method for elliptic problems. P. Ciarlet, SIAM 2002.