Lectures:	MW 3:30-4:50, room 121 RAI
Professor:	Anne Greenbaum, C-434 Padelford, 543-1175
Office Hours:	MW after class - 6:00, or by appointment or drop in.
e-mail:	greenbau@math.washington.edu
Web Address:	http://www.math.washington.edu/~greenbau
	Course materials: Click on ``Math/AMath 595".

Text: Numerical solution of partial differential equations by the finite element method, by Claes Johnson, Cambridge University Press, 1987. (available at Professional Copy 'n' Print, 4200 University Way NE)

Reserve list: The following books are on reserve in the Mathematics Research Library or are available in the Engineering Library.

1. The Mathematical Theory of Finite Element Methods by Susanne C. Brenner and L. Ridgway Scott (1994).

2. The Finite Element Method for Elliptic Problems by Philippe G. Ciarlet (1978).

3. An Analysis of the Finite Element Method by Gilbert Strang and George J. Fix (1973).

The course will cover:

1. Introduction to FEM for elliptic problems: Variational formulation of a one-dimensional model problem; generating a finite element approximation with piecewise linear functions; an error estimate for the model problem; the Hilbert spaces L₂ ( W), H¹ ( W), and H₀¹ ( W); natural and essential boundary conditions.

2. Abstract formulation of the finite element method for elliptic problems: Generating a finite element approximation in two and more dimensions; new problems encountered; regularity requirements; some finite element spaces; error analysis for elliptic problems; the energy norm and the L₂ ( W)-norm.

3. Some applications to elliptic problems.

4. Direct and iterative methods for solving the systems of linear equations arising from finite element approximations: Gaussian elimination; operation counts; band matrices; the frontal method; nested dissection; the conjugate gradient method; condition number of the stiffness matrix; preconditioning; multigrid methods.

5. FEM for parabolic and hyperbolic problems: semi-discretization in space; adaptive methods in space and time.

There will be weekly homework assignments (with some programming) and a course project. The project may involve using the finite element method to solve a problem of your choice, reading and reporting on a paper concerning aspects of the finite element method beyond those covered in class, etc.