# Article

 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 Year: 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 Stable URL: http://hdl.handle.net/10338.dmlcz/702917 .

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