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＜電子ブック＞
Numerical solution of Variational Inequalities by Adaptive Finite Elements / by Franz-Theo Suttmeier
(Advances in Numerical Mathematics)

版	1st ed. 2008.
出版者	(Wiesbaden : Vieweg+Teubner Verlag : Imprint: Vieweg+Teubner Verlag)
出版年	2008
本文言語	英語
大きさ	X, 161 p : online resource
著者標目	*Suttmeier, Franz-Theo author SpringerLink (Online service)
件　名	LCSH:Numerical analysis LCSH:Mathematics FREE:Numerical Analysis FREE:Mathematics
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-8348-9546-2

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