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This work describes a general approach to a posteriori error estimation and adaptive mesh design for ?nite 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 - merically computed dual solution. The resulting local error indicators are used in a feed-back process for generating economical meshes which are tailored - cording 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. F¨ ur Alexandra, Katharina und Merle Contents 1 Introduction 1 2 Models in elasto-plasticity 13 2. 1 Governing equations . . . . . . . . . . . . . . . . . . . . . . . . 14 2. 2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3 The dual-weighted-residual method 23 3. 1 A model situation in plasticity . . . . . . . . . . . . . . . . . . 24 3. 2 A posteriori error estimate . . . . . . . . . . . . . . . . . . . . . 25 3. 3 Evaluation of a posteriori error bounds . . . . . . . . . . . . . . 26 3. 4 Strategies for mesh adaptation . . . . . . . . . . . . . . . . . . 28 3. 5 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 4 Extensions to stabilised schemes 33 4. 1 Discretisation for themembrane-problem . . . . . . . . . . . . 35 4. 2 A posteriori error analysis . . . . . . . . . . . . . . . . . . . . . 37 4. 3 Numerical tests . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Table of contents (15 chapters)
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Front Matter
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Back Matter
About the author
Dr. Franz-Theo Suttmeier is a professor of Scientific Computing at the Institute of Applied Analysis and Numerics at the University of Siegen.
Bibliographic Information
Book Title: Numerical solution of Variational Inequalities by Adaptive Finite Elements
Authors: Franz-Theo Suttmeier
Series Title: Advances in Numerical Mathematics
DOI: https://doi.org/10.1007/978-3-8348-9546-2
Publisher: Vieweg+Teubner Verlag Wiesbaden
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH, Wiesbaden 2008
Softcover ISBN: 978-3-8348-0664-2Published: 28 August 2008
eBook ISBN: 978-3-8348-9546-2Published: 12 March 2009
Series ISSN: 1616-2994
Edition Number: 1
Number of Pages: X, 161
Topics: Numerical Analysis, Mathematics, general