Adaptive Numerical Methods for Operator Equations
(dt. Adaptive Numerische Verfahren für Operatorgleichungen)
|Level, degree of commitment in original study programme||Advanced module, compulsory elective module|
|Forms of teaching and learning,
|Lecture (3 SWS), recitation class (1 SWS), |
180 hours (60 h attendance, 120 h private study)
Course requirement: Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination
|German,The grading is done with 0 to 15 points according to the examination regulations for study course M.Sc. Mathematics.|
|Original study programme||M.Sc. Mathematik / Vertiefungsbereich Mathematik|
|One semester, |
|Person in charge of the module's outline||Prof. Dr. Stephan Dahlke|
- Elliptic partial differential equations
- weak solutions
- Galerkin method
- finite elements
- a-posteriori error estimators
- adaptive refinement strategies
- Wavelets, compressibility
The students shall
- To recognize the relevance of adaptive approximation techniques for practical problems, especially for the numerical treatment of elliptic partial differential equations, and to acquire knowledge of the basic principles of error estimator design and refinement strategies,
- learn how methods from functional analysis, numerical analysis and approximation theory interact,
- Re-evaluate knowledge from basic and advanced modules,
- practice mathematical working methods (development of mathematical intuition and its formal justification, training of the ability to abstract, proof techniques),
- improve their oral communication skills in the exercises by practicing free speech in front of an audience and during discussion.
None. The competences taught in the following modules are recommended: either Foundations of Mathematics and Linear Algebra I and Linear Algebra II or Basic Linear Algebra, either Analysis I and Analysis II or Basic Real Analysis, Numerical Analysis.
- - Theorie und Numerik elliptischer Differentialgleichungen, W. Hackbusch, Teubner Studienbücher (1996)
- - Numerical Analysis of Wavelet Methods, A. Cohen, North-Holland (2003)
- - A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques, R. Verführt, Wiley Series Advances in Numerical Mathematics. Chichester: Wiley. Stuttgart: B.G. Teubner (1996)
- - Adaptive Approximations- und Diskretisierungsverfahren, T. Raasch, Vorlesungsskript, Universität Mainz (2009)
This page describes a module according to the latest valid module guide in Wintersemester 2020/21. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:
- WiSe 2016/17 (no corresponding element)
- SoSe 2018 (no corresponding element)
- WiSe 2018/19
- WiSe 2019/20
- WiSe 2020/21
- SoSe 2021
- WiSe 2021/22
- WiSe 2022/23
The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.
The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.