# Computational Methods 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]