FEM_2014, Fall Session 2014


Lectures are in room 468, 2:00-3:00pm. Problem sessions are held in 445 DSL (Burkardt) or 456 DSL (van Wyk) or room 468 (seminar room) as convenient.

  1. Wednesday, 27 August:
    Class organization
  2. Monday, 01 September:
    Problem Sesssion (Room 445)
  3. Wednesday, 03 September
    Lecture: Approximate Solution of a Boundary Value Problem; a partial differential equation u''=f with boundary conditions. derivation of the weak form; a discrete space Vh; representation of the discrete solution as a linear combination of basis functions; the piecewise linear discrete space; generating the linear system.
  4. Monday, 08 September:
    Problem Sesssion (Room 445)
  5. Wednesday, 10 September:
    Lecture: the stiffness matrix K and mass matrix M arise from the variational formulation; how the system matrix A is formed from K and M; symmetric positive definiteness; K and L and M for the hat function basis.
  6. Monday, 15 September:
    Problem Sesssion (Room 445)
  7. Wednesday, 17 September:
    Lecture: the formula for the L matrix; building the linear system by elements, rather than by nodes; approximating integrals by quadrature; discussion of the 1D Python program; vector norms; orthogonality; the error norm; convergence; convergence rates.
  8. Monday, 22 September:
    Problem Sesssion (Room 445)
  9. Wednesday, 24 September:
    Lecture: the L2 norm, H1 semi-norm, and Energy norm; expected error norm decay rates; computing a table of values, the L2 norm, the H1 semi-norm, and the average value of the solution;
  10. Monday, 29 September:
    Problem Sesssion (Room 445)
  11. Wednesday, 01 October:
    Lecture (van Wyk): using FENICS to set up and solve a 1D problem.
  12. Friday, 03 October:
    Problem session (Burkardt): on computing the L2 norm and H1 semi-norm of the finite element error.
  13. Monday, 06 October:
    Problem Sesssion (Room 445)
  14. Wednesday, 08 October:
    Lecture (van Wyk/Burkardt): the finite element interpolant, and its use in FENICS (and homework); writing a mesh to an XML file, modifying mesh files by hand to perform refinement, using a mesh that is stored in a file.
  15. Monday, 13 October:
    Problem Sesssion (Room 445)
  16. Wednesday, 15 October:
    Welcome visitor Qingguang Guan!
    Lecture: the mathematical formulation of elliptic problems in 2D; the finite element formulation in 2D; a simple bilinear mesh for the 2D problem.
  17. Monday, 20 October:
    Problem Sesssion, 2pm-3pm, (Burkardt, Room 445)
  18. Wednesday, 22 October:
    Lecture: generating a mesh with Gmsh / Triangle / Mesh2D. Storing a mesh in a file. The XML mesh file format used by FENICS.
  19. Monday, 27 October:
    Problem Sesssion, 2pm-3pm, (Burkardt, Room 445)
  20. Wednesday, 29 October:
    Lecture (van Wyk): The equations of potential flow. Solving a potential flow problem using a region defined by an XML mesh file.
  21. Monday, 03 November:
    Theory Sesssion, 2:45pm-3:45pm (note time change!), (van Wyk, Room 468), Bilinear forms: Galerkin projection, best approximation.
  22. Wednesday, 05 November:
    Lecture: the steady heat equation; the steady Burgers equation
  23. Monday, 10 November:
    Theory Sesssion, 2:45pm-4:15pm, (van Wyk, Room 468), Riesz Representation, when the bilinear form is equivalent to a norm, the weak derivative, the space H^m and its norm
  24. Wednesday, 12 November:
    Lecture: the time dependent heat equation
  25. Monday, 17 November:
    Theory Sesssion, 2:45pm-3:45pm, (van Wyk, Room 468), Sobolev spaces, the Lax-Milgram theorem, Cea's Lemma.

  26. Wednesday, 19 November:
    Lecture (Burkardt/van Wyk): the time dependent heat equation (last chance), the steady Stokes flow problem for velocity and pressure; defining a function space for (u,p); setting boundary conditions; the variational form; special treatment of the linear system
  27. Monday, 24 November:
    Theory Sesssion:
  28. Wednesday, 26 November:
  29. Monday, 01 December:
    Theory Sesssion:
  30. Wednesday, 03 December:
    Lecture: Navier-Stokes problems

You can return to the FEM 2014 web page.

Last revised on 19 November 2014.