Numerical solution of Variational Inequalities by Adaptive Finite Elements (Advances in Numerical Mathematics)

Suttmeier, Franz-Theo

ISBN 10: 3834806641 / ISBN 13: 9783834806642

Editore: Vieweg+Teubner Verlag, 2008

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Dati bibliografici

• Titolo: Numerical solution of Variational Inequalities by Adaptive Finite Elements (Advances in Numerical Mathematics)
• Editore: Vieweg+Teubner Verlag
• Data di pubblicazione: 2008
• Lingua: Inglese
• ISBN 10: 3834806641
• ISBN 13: 9783834806642
• Rilegatura: Brossura
• Condizione: New

Descrizione articolo

Riassunto

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.

Informazioni sull?autore

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