M. Weiser

- First lecture: October 21, first practice seminar: October 24
- Lecture on December 9 canceled
- Practice seminar on November 7 and 14 canceled

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

Lecture | Mo 10-12 | SR 119, Arnimallee 3 | M. Weiser |

Exercise | Do 16-18 | SR 140, Arnimallee 7 | M. Weiser |

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

Secretariat | ZIB 4025 | E. Körnig |

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.
- Inside Finite Elements. de Gruyter. 2016.
- 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 October 28

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

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

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

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

11.11. | 2D Grids, elemental matrices, assembly |

18.11. | direct solvers: band, AMD ordering |

25.11. | nested dissection |

02.12. | classical iterative methods, gradient method |

09.12. | --- canceled --- |

16.12. | a posteriori error estimates |

06.01. | higher order FE |

13.01. | quadrature, error estimation |

20.01. | marking and mesh refinement |

27.01. | grid hierachies and multigrid |

03.02. | multigrid |

10.02. | tba |

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