Numerical solution of Variational Inequalities by Adaptive Finite Elements (Paperback)

Franz-Theo Suttmeier

ISBN 10: 3834806641 / ISBN 13: 9783834806642

Editore: Springer Fachmedien Wiesbaden, Weisbaden, 2008

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Paperback. 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . 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. 2 A posteriori error estimate . 3 Evaluation of a posteriori error bounds . 2 A posteriori error analysis . Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.

Codice articolo 9783834806642

Dati bibliografici

• Titolo: Numerical solution of Variational Inequalities by Adaptive Finite Elements (Paperback)
• Editore: Springer Fachmedien Wiesbaden, Weisbaden
• Data di pubblicazione: 2008
• Lingua: Inglese
• ISBN 10: 3834806641
• ISBN 13: 9783834806642
• Rilegatura: Paperback
• 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.