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Numerical solution of Variational Inequalities by Adaptive Finite Elements [electronic resource] /by Franz-Theo Suttmeier.

by Suttmeier, Franz-Theo [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookPublisher: Wiesbaden : Vieweg+Teubner, 2008.Description: X, 161p. 51 illus., 10 illus. in color. online resource.ISBN: 9783834895462.Subject(s): Mathematics | Mathematics | Mathematics, generalDDC classification: 510 Online resources: Click here to access online
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.
In: Springer eBooksSummary: 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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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.

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