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This entry is from Winter semester 2021/22 and might be obsolete. No current equivalent could be found.

Adaptive Numerical Methods for Operator Equations
(dt. Adaptive Numerische Verfahren für Operatorgleichungen)

Level, degree of commitment Specialization module, compulsory elective module
Forms of teaching and learning,
workload		 Lecture (3 SWS), recitation class (1 SWS),
180 hours (60 h attendance, 120 h private study)
Credit points,
formal requirements		 6 CP
Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination
Language,
Grading		 German,
The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Mathematics.
Duration,
frequency		 One semester,
irregular
Person in charge of the module's outline Prof. Dr. Stephan Dahlke

Contents

  • Elliptic partial differential equations
  • weak solutions
  • Galerkin method
  • finite elements
  • a-posteriori error estimators
  • adaptive refinement strategies
  • Wavelets, compressibility

Qualification Goals

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.

Prerequisites

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.


Applicability

Module imported from M.Sc. Mathematics.

It can be attended at FB12 in study program(s)

  • B.Sc. Mathematics
  • B.Sc. Business Mathematics
  • M.Sc. Computer Science
  • M.Sc. Mathematics
  • M.Sc. Business Mathematics

When studying M.Sc. Business Mathematics, this module can be attended in the study area Specialization and Practical Modules in Mathematics.

The module is assigned to Applied Mathematics. Further information on eligibility can be found in the description of the study area.


Recommended Reading

  • 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)



Please note:

This page describes a module according to the latest valid module guide in Winter semester 2021/22. 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:

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.