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]