Numerical solution of Variational Inequalities by Adaptive Finite Elements
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...
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oai:localhost:123456789-1298532023-07-17T15:13:22Z Numerical solution of Variational Inequalities by Adaptive Finite Elements Suttmeier, Franz-Theo. SpringerLink (Online service) Matemática. 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. 0 2022-10-06T07:52:29Z 2022-10-06T07:52:29Z 2008. Digital 51 S967n 9783834895462 197941 http://dx.doi.org/10.1007/978-3-8348-9546-2 http://dx.doi.org/10.1007/978-3-8348-9546-2 |
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Matemática. |
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Matemática. Suttmeier, Franz-Theo. SpringerLink (Online service) Numerical solution of Variational Inequalities by Adaptive Finite Elements |
| description |
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. |
| format |
Digital |
| author |
Suttmeier, Franz-Theo. SpringerLink (Online service) |
| author_facet |
Suttmeier, Franz-Theo. SpringerLink (Online service) |
| author_sort |
Suttmeier, Franz-Theo. |
| title |
Numerical solution of Variational Inequalities by Adaptive Finite Elements |
| title_short |
Numerical solution of Variational Inequalities by Adaptive Finite Elements |
| title_full |
Numerical solution of Variational Inequalities by Adaptive Finite Elements |
| title_fullStr |
Numerical solution of Variational Inequalities by Adaptive Finite Elements |
| title_full_unstemmed |
Numerical solution of Variational Inequalities by Adaptive Finite Elements |
| title_sort |
numerical solution of variational inequalities by adaptive finite elements |
| publishDate |
2022 |
| url |
http://dx.doi.org/10.1007/978-3-8348-9546-2 |
| work_keys_str_mv |
AT suttmeierfranztheo numericalsolutionofvariationalinequalitiesbyadaptivefiniteelements AT springerlinkonlineservice numericalsolutionofvariationalinequalitiesbyadaptivefiniteelements |
| _version_ |
1771689195542151168 |