# Numerical solution of Variational Inequalities by Adaptive Finite Elements

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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.

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.

A Posteriori Fehlerschätzung A Priori Fehlerschätzung Adaptivität Finite Finite-Elemente-Methode Variationsungleichungen equation finite element method mathematics

- DOI https://doi.org/10.1007/978-3-8348-9546-2
- Copyright Information Vieweg+Teubner Verlag | GWV Fachverlage GmbH, Wiesbaden 2008
- Publisher Name Vieweg+Teubner
- eBook Packages Mathematics and Statistics
- Print ISBN 978-3-8348-0664-2
- Online ISBN 978-3-8348-9546-2
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