## lectures |

Here is a list of lecture notes and projects used mainly for the course Math 226: Computational PDEs in UC Irvine. I try to strike a good balance between mathematical theory and programming skill. Welcome to send me your comments (e.g. typos, mistakes, notation inconsistence, suggestion, and even complains) on the lecture notes.

- Introduction
- Finite Difference Methods
- Programming of Finite Difference Methods
**Project**: Finite Difference Method.- Finite Volume Methods

- Sobolev Spaces
- Finite Element Methods
- Programming of Finite Element Methods
**Project**: Finite Element Method.- Adaptive Finite Element Methods

- Conjugate Gradient Methods
- Classical Iterative Methods
- Subspace Correction and Auxiliary Space Methods

- Multigrid Methods
- Programming of Multigrid Methods
**Project**: Multigrid Methods.- Recrusive Proofs of Multigrid Methods

- Quick sort and Merge sort
- FFT (Fast Fourier Transform)
- Fast Multipole Methods
**Project**: Fast Multipole Methods.

- Brief introduction to Navier-Stokes equation
- Finite element methods for Stokes equations
**Project**: Finite element methods for Stokes Equations.- MAC scheme for Stokes equations
- Programming of MAC Scheme for Stokes Equations
**Project**: MAC scheme for Stokes Equations.- Fast solvers for Stokes equations