## 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
- Classic theory
- Existence of global minimums
- Hamilton Jacobi theory
- Constraint Variation Problems
- Noether's theory

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

- Introduction to Adaptive Finite Element Methods
- Convergence Theory of Adaptive Finite Element Methods
- Data Structure for Triangulations

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

- Introduction to 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.

- Finite Differnce Methods for Parabolic Equations
- Finite Element Methods for Parabolic Equations
**Project**: Heat Equations.

- 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

- Introduction to Linear Elasticity
- Variational Formulation of Linear Elasticity
- Tensor Calculus
- Finite Element Methods for Linear Elasticity
**Project**: ERobust Finite Element for Linear Elasticity