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Numerical solution of variational inequalities by adaptive finite elements

Author: Franz-Theo Suttmeier
Publisher: Wiesbaden : Vieweg+Teubner Research, ©2008.
Series: Wiley-Teubner series, advances in numerical mathematics.
Edition/Format:   eBook : Document : English : 1st edView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Suttmeier, Franz-Theo.
Numerical solution of variational inequalities by adaptive finite elements.
Wiesbaden : Vieweg+Teubner Research, ©2008
(OCoLC)297287361
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Franz-Theo Suttmeier
ISBN: 9783834895462 3834895466 3834806641 9783834806642
OCLC Number: 325000443
Target Audience: Students and researchers from the field of numerical mathematics, and users of adaptive finite element techniques.
Description: 1 online resource (x, 161 pages) : illustrations (some color).
Contents: Models in elasto-plasticity --
The dual-weighted-residual method --
Extensions to stabilised schemes --
Obstacle problem --
Signorini's problem --
Strang's problem --
General concept --
Lagrangian formalism --
Obstacle problem revisited --
Variational inequalities of second kind --
Time-dependent problems --
Applications --
Iterative Algorithms --
Conclusion.
Series Title: Wiley-Teubner series, advances in numerical mathematics.
Responsibility: Franz-Theo Suttmeier.

Abstract:

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.

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