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This entry is from Winter semester 2016/17 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): Written or oral examination
Examination type: Successful completion of at least 50 percent of the points from the weekly exercises.
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

Students should be able to

  • Recognize the relevance of adaptive approximation methods for practical problems, especially for the numerical treatment of elliptic partial differential equations, and acquire knowledge of the basic principles of designing error estimators and refinement strategies.
  • learn how methods from functional analysis, numerics, and approximation theory work together
  • re-evaluate knowledge from basic and advanced modules
  • practice mathematical working methods (developing mathematical intuition and its formal justification, training of abstraction skills, reasoning)
  • improve their oral communication skills in the exercises by practicing free speech in front of an audience and in discussion

Prerequisites

Translation is missing. Here is the German original:

Keine. Empfohlen werden die Kompetenzen, die in den Basismodulen und im Modul Numerik (Numerische Basisverfahren) vermittelt werden.


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 B.Sc. Mathematics, this module can be attended in the study area Compulsory Elective Modules in Mathematics.

Die Wahlmöglichkeit des Moduls ist dadurch beschränkt, dass es der Angewandten Mathematics zugeordnet ist.


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 2016/17. 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.