Adaptive Finite Element Methods (Wintersemester 2007/08)
- Dozent*in: Prof. Dr. Willy Dörfler
- Veranstaltungen: Vorlesung (1091)
- Semesterwochenstunden: 2
- Hörerkreis: Mathematik (ab 7. Semester)
Termine | ||
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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.
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.