Math 226A Fall 2011

Math 266A Computational PDE

Meeting Information

• Room: RH 192
• Day & time: Tu Th 11:00 am - 12:20 pm

Project and Homework

• Homework 1: Finite Difference Method. Due date: Oct 3.
• Homework 2: Finite Element Method. Due date: Oct 13.
• Project 1: Linear Finite Element Method. Due date: Oct 31.
• Homework 3: Error Analysis of FEM. Due date: Nov 8.
• Project 2: Nonlinear Poisson Boltzmann Equation. Due date: Nov 21.
• Homework 4: Iterative Methods. Due date: Dec 5.
• Project 3: Multigrid Methods. Due date: Dec 12.

Syllabus

In Math 226 A, we shall focus on numerical solutions for the elliptic equations. Parabolic and hyperbolic equations will be discussed in 226 B and C, respectively. More precisely, we plan to cover the following topics:

• Finite element methods for linear elliptic equations
• Finite difference and finite volume methods
• Sobolev spaces and elliptic equations
• Nonlinear elliptic equations
• Fast solvers: Conjugate Gradient method and multigrid method
• Adaptive finite element methods

A pdf version of the syllabus can be downloaded from here.

References

Lecture Notes will be distributed in class. But the following books are good references for reading:

• Gilbert Strang. Computational Science and Engineering, Wellesley-Cambridge Press, 2007. Watch viedos in iTunes U.
• Gilbert Strang and George Fix. An Analysis of the Finite Element Method. Wellesley-Cambridge Press (1973). Second Edition (2008).
• S.C. Brenner and L.R. Scott. The mathematical theory of finite element methods, vol. 15 of Texts in Applied Mathematics, Springer-Verlag, New York, second edition, 2002.

Grading

Your course grade will be determined by your cumulative average at the end of the term:

• 40% Homework
• 40% Matlab projects
• 20% Final Exam/Project

Lecture Notes

Welcome to send me your comments (e.g. typos, mistakes, notation inconsistence, suggestion, and even complains) on the lecture notes.

• Introduction
• Finite Difference Methods
• Finite Element Methods
• Sobolev Spaces
• Programming of Finite Element Methods
• Finite Volume Methods
• Unified Error Analysis
• Adaptive Finite Element Methods
• Nonlinear Elliptic PDE
• Methods of Subspace Correction
• Multigrid Methods