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Arbeitsgruppe 2: Numerik partieller Differentialgleichungen

Sekretariat
Kollegiengebäude Mathematik (20.30)
Zimmer 3.012

Adresse
Hausadresse:
Zimmer 3.012
Mathematikgebäude (20.30)
Englerstraße 2
D-76131 Karlsruhe

Postadresse:
Institut für Angewandte und
Numerische Mathematik 2
Karlsruher Institut für Technologie (KIT)
D-76049 Karlsruhe

Öffnungszeiten:
Mo. bis Do.: 10:00-11:30 Uhr

Tel.: 0721 608 42680

Fax.: 0721 608 46679

Adaptive Finite Element Methods (Wintersemester 2007/08)

Dozent: Prof. Dr. Willy Dörfler
Veranstaltungen: Vorlesung (1091)
Semesterwochenstunden: 2
Hörerkreis: Mathematik (ab 7. Semester)


Termine
Vorlesung: Montag 11:30-13:00 Seminarraum 33

The Finite Element Method is the method of choice for the solution
of elliptic boundary value problems.
In computing these approximations we follow two aims:

* we need a computable error bound to judge the quality of an approximation,
* we want to reduce the amount of work to obtain an approximation of a prescribed tolerence.

The first item is a must since numerical simulations without information about their accuracy
are dangerous. This has been seen by some failures in the past, see information about the
Sleipner accident on

http://www.ima.umn.edu/~arnold/disasters/disasters.html.

The latter aim may be achieved by constructing local (e.g. in space) error indicators
and perform local refinement where large errors are indicated.
We show for a model problem how to construct convergent local refinement algorithms and show that
the algorithm has optimal complexity. Current research considers the application of high oder methods
and non-standard basis functions.

Adaptive Verfeinerung

This lecture is part of the education of the International Masterprogramme and the Graduiertenkolleg 1294.

Literature.

  • Ainsworth, M. and Oden, J. T.: A Posteriori Error Estimation in Finite Element Analysis. John Wiley, New York, 2000.
  • Schwab, Chr.: p- and hp-finite element methods. Theory and applications in solid and fluid mechanics}}. Clarendon Press, Oxford, 1998.
  • Verfuerth, R.: A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques. Wiley-Teubner, Chichester, 1996.