M. Weiser

- Results of written exam
**available**.

Matr.-Nr. Points (max 40) Grade 4827773 36 1.3 4905257 23 3.3 4359900 21 3.7

What | When | Where | Who |
---|---|---|---|

Lecture | Mo 16-18 | SR 009, Arnimallee 4-6 | M. Weiser |

Exercise | Fr 14-16 | SR 009, Arnimallee 4-6 | M. Weiser |

Office hour | just ask | ZIB 4309 | M. Weiser |

Secretariat | ZIB 4025 | Körnig/Kussack |

All relevant implementation aspects of finite element methods are discussed in this course. The focus is on algorithms and data structures as well as on their concrete implementation. Theory is only covered as far as it gives insight into the construction of algorithms. In the homework, a complete FE-solver for scalar 2D problems will be implemented in Matlab/Octave.

- Numerische Mathematik 3. Adaptive Lösung partieller Differentialgleichungen. de Gruyter. 2011.
- C. Grossmann, H.-G. Roos: Numerische Behandlung partieller Differentialgleichungen
- D. Braess: Finite Elemente
- J.-L. Guermond, A. Ern: Theory and Practice of Finite Elements

In-depth treatment, in particular part III on FE realization is relevant - J. Fish, T. Belytschko: A First Course in Finite Elements

Introductory text from an engineering point of view, almost no realization of FE. - C. Johnson: Numerical Solution of Partial Differential Equations by the Finite Element Method

Classic introductory textbook. - H.R. Schwarz: Finite Element Methods

Classic textbook.

- Exercise due to April 24
- Exercise due to May 8
- Exercise due to May 15
- Exercise due to May 22

- Exercise due to May 29
- Exercise due to June 5
- Exercise due to June 12
- Exercise due to June 19
- Exercise due to June 26

Use quadrature rule points and weights. - Exercise due to July 3
- Exercise due to July 10

When | What |
---|---|

14.04. | Basic equations prototypes, boundary conditions, classification. classical results |

16.04. | Variational formulation of elliptic equations minimization, boundary conditions, Weierstrass, Lax-Milgram |

24.04. | Finite Elements 1D, elemental matrices, assembly |

01.05. | --- canceled --- |

08.05. | 2D Grids, elemental matrices, assembly |

15.05. | direct solvers: band, AMD ordering |

22.05. | nested dissection |

29.05. | classical iterative methods, gradient method |

05.06. | a posteriori error estimates |

12.06. | higher order FE |

19.06. | quadrature, error estimation |

26.06. | marking and mesh refinement |

03.07. | grid hierachies and multigrid |

10.07. | multigrid |

17.07. | written exam |

- regular participance at the exercises
- i.e., show up often enough
- active participance at the exercises
- Solve homework tasks and earn 50% of points in both first and second half of term.
- written exam
- Achieve 50% of points.