Math 595A: Special Topics in Numerical Analysis:
Finite Element Methods
Anne Greenbaum
Winter 2001, Monday/Wednesday 3:30-4:45
This course will cover practical aspects and theory of finite element
methods for the numerical solution of partial differential equations.
Topics to be covered include: the finite element method for elliptic
problems, some finite element spaces, approximation theory and error estimates
for elliptic problems. Some mention will be made of uses of finite element
methods in solving parabolic and hyperbolic problems as well. We
also will cover some practical aspects of the implementation of finite
element methods, including iterative methods, such as multigrid methods,
for solving the resulting linear systems.
In addition to regular homework assignments, students will do a project
involving the implementation of a finite element method for solving a physical
problem of interest.
The text will be: Numerical Solution of Partial Differential Equations
by the Finite Element Method, by Claes Johnson, Cambridge University
Press, 1987. Other relevant books on the subject include: An
Analysis of the Finite Element Method, by Strang and Fix; The Finite
Element Method for Elliptic Problems, by P.G. Ciarlet; and The Mathematical
Theory of Finite Element Methods, by Brenner and Scott.