**Instructor:**
Jon Wilkening

**Lectures:** TuTh 11-12:30pm, Room 7 Evans

**Course Control Number:** 54967

**Office:** 1091 Evans

**Office Hours:** Monday 11AM-1PM

**Prerequisites:** Math 128A or equivalent knowledge of
basic numerical analysis. Some programming experience (e.g.
Matlab, Fortran, C, or C++)

**Required Texts:**

Morton and Mayers, Numerical Solution of Partial Differential Equations

Dietrich Braess, Finite Elements: Theory, Fast Solvers, and Applications
in Solid Mechanics

**Recommended Reading:**

John C. Strikwerda, Finite difference schemes and partial differential
equations, (on 1 day reserve, math library)

R. J. LeVeque, Numerical methods for conservation laws,
(on 1 day reserve, math library)

**Syllabus:** In the first half of the course, we will study
finite difference methods for solving hyperbolic and parabolic partial
differential equations. I will describe von Neumann stability
analysis, CFL conditions, the Lax-Richtmeyer equivalence theorem
(consistency + stability = convergence), dissipation and dispersion.
We will use these tools to analyze several popular schemes
(Lax-Wendroff, Lax-Friedrichs, leapfrog, Crank-Nicolson, ADI, etc.)
The second half of the course will be devoted to finite element
methods for elliptic equations (Poisson, Lamé, Stokes). We will
discuss Sobolev spaces, functional analysis, the Lax-Milgram theorem,
Cea's lemma, the Bramble-Hilbert lemma, variational calculus, mixed
methods for saddle point problems, and the Babuska-Brezzi inf-sup
condition. If time permits, I'll also talk about hyperbolic conservation
laws in the first part of the course and least squares finite elements
in the second part.

**Course Webpage:** http://math.berkeley.edu/~wilken/228B.S07

**Grading:** Grades will be based entirely on homework.

**Homework:** 8 assignments

**Comments:** Homework problems will be graded Right/Wrong, but
you may resubmit the problems you get Wrong * within two weeks *
of getting them back to convert them to Right. (If you turn in a
homework late, you forfeit this possibility).