# Computational Methods (January-April, 2013)

## Slides used in class

- List of references texts [pdf]
- Introduction [pdf]
- Finite difference method [pdf]
- Finite difference method for elliptic equation I [pdf]
- Finite difference method for elliptic equation II [pdf]
- Finite difference method for elliptic equation III [pdf]
- Finite volume method for BVP: Discontinuous coefficients and high Peclet number [pdf]
- Finite difference method for 1-D heat equation [pdf]
- Finite difference method for 2-D heat equation [pdf]
- Finite difference method for 1-D linear convection equation [pdf]
- High order method for 1-D linear convection equation [pdf]
- Introduction to non-linear conservation laws [pdf]
- FVM for non-linear conservation law I [pdf]
- FVM for non-linear conservation law II [pdf]
- FVM for non-linear conservation law III [pdf]
- FVM for non-linear conservation law IV [pdf]
- FVM for non-linear conservation law V [pdf]
- FVM for non-linear conservation law: Approximate Riemann solvers [pdf]
- FVM for non-linear conservation law: Second order extension [pdf]
- FEM for BVP: 1D case [pdf]
- Lagrange interpolation and error estimates [pdf]
- Galerkin method [pdf]
- FEM programming [pdf]
- A posteriori error estimation for elliptic problems [pdf]
- FEM for heat equation [pdf]
- FEM for convection dominated problem [pdf]

## Assignments

- Assignment 1 [pdf]
- Assignment 2 [pdf]
- Assignment 3 [pdf]: Solution matlab program [peaceman_rachford.m]

## Computer programs

- 1-D boundary value problem [bvp_1d.m]
- 2-D poisson equation [Jacobi, Gauss-Seidel, SOR]
- 1-D convection diffusion equation using FVM: [centered, upwind]
- 1-D heat equation using FDM [FTCS, BTCS, Crank-Nicholson]
- 1-D linear convection equation: [periodic solution, discontinuous solution]
- 1-D inviscid burgers equation [conlaw.m]

## Notes

- Notes on conservation laws by Prof. S. Baskar [pdf]
- Lectures on the Finite Element Method by Ph. Ciarlet [pdf]