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Title: Finite element analysis for a regularized variational inequality of the second kind (English)
Author: Zhang, Tie
Author: Zhang, Shuhua
Author: Azari, Hossein
Language: English
Journal: Applications of Mathematics 2012
Volume: Proceedings. Prague, May 2-5, 2012
Issue: 2012
Pages: 317-331
Category: math
Summary: In this paper, we investigate the a priori and the a posteriori error analysis for the finite element approximation to a regularization version of the variational inequality of the second kind. We prove the abstract optimal error estimates in the $H^1$- and $L_2$-norms, respectively, and also derive the optimal order error estimate in the $L_\infty$-norm under the strongly regular triangulation condition. Moreover, some residual--based a posteriori error estimators are established, which can provide the global upper bounds on the errors. These a posteriori error results can be applied to develop the adaptive finite element methods. Finally, we supply some numerical experiments to validate the theoretical results. (English)
Keyword: finite element approximation
Keyword: a priori error estimates
Keyword: a posteriori error estimates
Keyword: numerical examples
Keyword: variational inequality
Keyword: stability
MSC: 49J40
MSC: 49M25
MSC: 65K15
MSC: 65N12
MSC: 65N15
MSC: 65N30
idZBL: Zbl 1313.65176
idMR: MR3204423
Date available: 2017-02-14T09:05:47Z
Last updated: 2017-04-13
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