Computational Methods (January-April, 2013)

Slides used in class

1. List of references texts [pdf]
2. Introduction [pdf]
3. Finite difference method [pdf]
4. Finite difference method for elliptic equation I [pdf]
5. Finite difference method for elliptic equation II [pdf]
6. Finite difference method for elliptic equation III [pdf]
7. Finite volume method for BVP: Discontinuous coefficients and high Peclet number [pdf]
8. Finite difference method for 1-D heat equation [pdf]
9. Finite difference method for 2-D heat equation [pdf]
10. Finite difference method for 1-D linear convection equation [pdf]
11. High order method for 1-D linear convection equation [pdf]
12. Introduction to non-linear conservation laws [pdf]
13. FVM for non-linear conservation law I [pdf]
14. FVM for non-linear conservation law II [pdf]
15. FVM for non-linear conservation law III [pdf]
16. FVM for non-linear conservation law IV [pdf]
17. FVM for non-linear conservation law V [pdf]
18. FVM for non-linear conservation law: Approximate Riemann solvers [pdf]
19. FVM for non-linear conservation law: Second order extension [pdf]
20. FEM for BVP: 1D case [pdf]
21. Lagrange interpolation and error estimates [pdf]
22. Galerkin method [pdf]
23. FEM programming [pdf]
24. A posteriori error estimation for elliptic problems [pdf]
25. FEM for heat equation [pdf]
26. FEM for convection dominated problem [pdf]

Assignments

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

Computer programs

1. 1-D boundary value problem [bvp_1d.m]
2. 2-D poisson equation [Jacobi, Gauss-Seidel, SOR]
3. 1-D convection diffusion equation using FVM: [centered, upwind]
4. 1-D heat equation using FDM [FTCS, BTCS, Crank-Nicholson]
5. 1-D linear convection equation: [periodic solution, discontinuous solution]
6. 1-D inviscid burgers equation [conlaw.m]

Notes

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