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.

EUDML-ID : urn:eudml:doc:287802
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Mots clés:

@article{702917,
     title = {Finite element analysis for a regularized variational inequality of the second kind},
     booktitle = {Applications of Mathematics 2012},
     series = {GDML\_Books},
     publisher = {Institute of Mathematics AS CR},
     address = {Prague},
     year = {2012},
     pages = {317-331},
     mrnumber = {MR3204423},
     zbl = {1313.65176},
     url = {http://dml.mathdoc.fr/item/702917}
}

Zhang, Tie; Zhang, Shuhua; Azari, Hossein. Finite element analysis for a regularized variational inequality of the second kind, dans Applications of Mathematics 2012, GDML_Books,  (2012), pp. 317-331. http://gdmltest.u-ga.fr/item/702917/