Numerical solution of Variational Inequalities by Adaptive Finite Elements

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Advances in Numerical Mathematics

ISBN: 3834806641
ISBN 13: 9783834806642
Autor: Suttmeier, Franz-Theo
Verlag: Springer Vieweg
Umfang: x, 161 S.
Erscheinungsdatum: 28.08.2008
Auflage: 1/2008
Produktform: Kartoniert
Einband: Kartoniert

Franz-Theo Suttmeier describes a general approach to a posteriori error estimation and adaptive mesh design for finite element models where the solution is subjected to inequality constraints. This is an extension to variational inequalities of the so-called Dual-Weighted-Residual method (DWR method) which is based on a variational formulation of the problem and uses global duality arguments for deriving weighted a posteriori error estimates with respect to arbitrary functionals of the error. In these estimates local residuals of the computed solution are multiplied by sensitivity factors which are obtained from a numerically computed dual solution. The resulting local error indicators are used in a feed-back process for generating economical meshes which are tailored according to the particular goal of the computation. This method is developed here for several model problems. Based on these examples, a general concept is proposed, which provides a systematic way of adaptive error control for problems stated in form of variational inequalities.

Artikelnummer: 4902232 Kategorie:

Beschreibung

The author presents a general approach to a posteriori error estimation and adaptive mesh design for finite element models where the solution is subjected to inequality constraints. The local weighted residuals, that result from an extension of the so-called Dual-Weighted-Residual method, are used in a feed-back process for generating economical meshes. Based on several model problems, a general concept is proposed, which provides a systematic way of adaptive error control for problems stated in form of variational inequalities.

Autorenporträt

Dr. Franz-Theo Suttmeier is a professor of Scientific Computing at the Institute of Applied Analysis and Numerics at the University of Siegen.

Herstellerkennzeichnung:


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E-Mail: juergen.hartmann@springer.com

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