Numerical Methods for Partial Differential Equations

Lecturer

Lecturer:        Prof. M. Grote

Assistant:       Y. Gleichmann

Contents

  • Numerical methods for partial differential equations (PDE)
  • Finite-Difference method (FD), Finite-Element method (FEM)
  • Convergence theory
  • Error estimates
  • Practical implementation

Prerequisites

  • Linear Algebra
  • Calculus
  • (real) Analysis
  • Introduction to Numerical Analysis
  • at least one Programming language (preferably MATLAB)

Dates

Course requirements

In order to obtain the 8 credit points for the lecture and the exercise class you have to fulfill the following criteria:

  • Theoretical exercises:
    • 2/3 of the total points obtained on the theoretical exercises. One point is given if the exercise is solved in a meaningful manner. On each exercise sheet there will be at most 3 points for theory.
    • Presenting the solution of one theoretical exercise at the blackboard at least once during the exercise class.
  • Programming excercises:
    • 2/3 of the total points obtained on the programming exercises. One point is given if the exercise is solved in a meaningful manner. On each exercise sheet there will at most 1 point for programming.
    • Presenting the solution of one programming exercise with the beamer at least once during the exercise class.

References

  • L. C. Evans, Partial Differential Equations
  • D. Braess, Finite Elemente
  • S. C. Brenner, L. R. Scott, The Mathematical Theory of Finite Element Methods
  • C. Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method
  • P. G. Ciarlet, The Finite Element Method for Elliptic Problems
  • Mats G. Larson, The Finite Element Method: Theory, Implementation, and Applications