Finite Elements and Calculus of Variations, 2003

Below find a list of the topics to be discussed in class. The references refer to the lecture notes to be handed out. During the semester the order of presentation may change, the changes should show on this page.

Main goal of this class:

Understand the basic mathematical background of the Finite Element Method (FEM) and some aspects of an efficent implementation on computers

Main topics to be discussed

Lecture notes and a tentative program

The lectures will be based on two sets of lecture notes A possible sequence of topics to be treated is
  1. The PDE for a heat equation [2]
  2. solving the heat equation, using FEMLAB
  3. From a minimization problem to a system of linear equations [1]
  4. a system of simple bars [1]
  5. 1-d Calculus of variations
  6. 1-d FEM for second order problems, a first attempt and an efficient algorithm
  7. 2-d calculus of variations
  8. 2-d FEM for second order problems
  9. coding in Octave, FEMoctave
  10. fast solvers for linear systems, Gauss, Cholesky, a sparse solver
  11. error estimates
  12. dynamic problems, heat and wave equation
  13. consistency, stability, convergence
Software to be used

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October, 2003 by
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