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Adaptive Finite Element Methods (Winter Semester 2007/08)

Lecture: Monday 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


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.


  • 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.