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Numerical solution of Variational Inequalities by Adaptive Finite Elements

  • Authors
  • Franz-Theo Suttmeier

Table of contents

  1. Front Matter
    Pages I-X
  2. Pages 1-12
  3. Pages 47-56
  4. Pages 57-68
  5. Pages 69-73
  6. Pages 75-79
  7. Pages 81-89
  8. Pages 105-107
  9. Pages 109-127
  10. Pages 129-139
  11. Pages 141-141
  12. Back Matter
    Pages 143-161

About this book

Introduction

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.

Keywords

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

Bibliographic information

  • 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
  • Buy this book on publisher's site