Math 228B - Numerical Solution of Differential Equations

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:

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).