Inside Finite Elements

WS 2019-2020, FU Berlin (VL 19216401, Ü 19216402)
M. Weiser

News

Dates and Rooms

WhatWhenWhereWho
LectureMo 10-12 SR 119, Arnimallee 3M. Weiser
ExerciseDo 16-18SR 140, Arnimallee 7M. Weiser
Office hourjust askZIB 4309M. Weiser
SecretariatZIB 4025E. Körnig

Contents

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 October 28

Reference Implementation

Syllabus

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

Exam

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