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, self-adjoint, second-order 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, Lax-Milgram lemma, approximation theory, error estimates, element construction, continuous, discontinuous, and mixed finite element methods, and solution methods for the resulting finite element systems.
The book Understanding and Implementing the Finite Element Method by Mark Gockenbach, SIAM 2006, will be used as a reference on implementation issues.
Written homework and several computational projects will be assigned. Suggested programming language is Matlab. The Matlab language provides extensive library of mathematical and scientific function calls entirely built-in. Matlab is available on Unix and Windows in the university computing labs. The full set of manuals is on the web in html and also in Adobe PDF format. The "Getting Started" manual is a good place to begin and is available both in html format and in Adobe PDF format. The full reference manual as well as manuals for each of the many toolboxes are all available.