Inside Finite Elements

SS 2015, FU Berlin (VL 19216401, Ü 19216402)
M. Weiser

News

Dates and Rooms

WhatWhenWhereWho
LectureMo 16-18 SR 009, Arnimallee 4-6M. Weiser
ExerciseFr 14-16SR 009, Arnimallee 4-6M. Weiser
Office hourjust askZIB 4309M. Weiser
SecretariatZIB 4025Körnig/Kussack

Contents

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.

Literature

Homework

  1. Exercise due to April 24
  2. Exercise due to May 8
  3. Exercise due to May 15
  4. Exercise due to May 22
  5. Exercise due to May 29
  6. Exercise due to June 5
  7. Exercise due to June 12
  8. Exercise due to June 19
  9. Exercise due to June 26
    Use quadrature rule points and weights.
  10. Exercise due to July 3
  11. Exercise due to July 10

Reference Implementation

Syllabus

The following schedule of topics is preliminary and subject to change.
WhenWhat
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

Exam

For completion of the module, the following conditions need to be fulfilled:
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.