Math 226B Winter 2012

Math 266B Computational PDE

Meeting Information

• Room: RH 440R
• Day & time: Tu Th 11:00 am - 12:20 pm
• Office hour: M W 11:00 am - 12:00 pm

Project and Homework

• Homework 1: Exercises in Lecture Notes 1, 2 and 3. Due date: Feb 2.
• Project 1: Finite element and difference methods for Stokes equations. Due date: Feb 9.
• Project 2: Fast Solvers for Stokes equations. Due date: Feb 29.
• Homework 2: Exercises in Lecture Notes on parabolic equations. Due date: Mar 6.
• Project 3: Transient Navier-Stokes Equations. Due date: Mar 19.
• Project 4: Edge element for Maxwell Equations. Due date: Mar 25.

Syllabus

In Math 226 B, we shall focus on numerical solutions for the parabolic and hyperbolic equations. More precisely, we will talk about numerical methods for solving

• Stokes equations
• Navier-Stokes equations
• Maxwell equations

References

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

• Elman.H, Silvester.D, and Wathen.A. Finite Elements and Fast Iterative Solvers with Applications in Incompressible Fluid Dynamics. 2005
• V.Girault and P.A. Raviart. Finite element methods for Navier-Stokes equations: Theory and algorithms, Springer-Verlag, Berlin, 1986.
• S. Larsson and V. Thomee. Partial Differential Equations with Numerical Methods, Springer, 2003.
• Gilbert Strang. Computational Science and Engineering, Wellesley-Cambridge Press, 2007. Watch viedos in iTunes U.
• P. Monk. Finite Element Methods for Maxwell Equations. Oxford University Press, New York, 2003.

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.

• Brief introduction to Navier-Stokes equation
• Inf-sup conditions
• Finite element method for Stokes equations
• Finite difference method (MAC) for Stokes equations
• Multigrid for Stokes equations
• Numerical Methods for Parabolic Equations
• Finite Element Methods for Maxwell Equations
• Multigrid for H(curl) and H(div) Problems