Computational Methods 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]