Math 226A Fall 2017

Math 266A Computational PDE

Meeting Information

• Room: RH 340P
• Day & time: M W F 10 - 10:50 am.
• Office hours: W F 11:10 - 12:00 pm.

Project and Homework

• Homework 1: Exercises in Lecture Notes for Finite Difference Methods.
  Due date: Oct 9.
• Project 1: Finite Difference Method. Due date: Oct 16.
• Homework 2: Exerxises in Lecture Notes for Finite Element Methods.
  Due date: Oct 23.
• Project 2: Finite Element Method. Due date: Oct 30.
• Homework 3: Iterative Methods. Due date: Nov 13.
• Project 3: Multigrid Methods. Due date: Nov 29.
• Final project: Nonlinear Poisson-Boltzman Equation. Due date: Dec 18.

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
• Fast solvers: Conjugate Gradient methods and multigrid methods
• Nonlinear elliptic equations

References

Lecture Notes can be found here. The following books are good references for reading:

• S. Larsson and V. Thomee, Partial Differential Equations with Numerical Methods, Springer, 2003.
• 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.
• A. Ern and J.-L. Guermond. Theory and Practice of Finite Elements, volume 159. Springer Science, 2013.

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