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Article

Zhang, Tie ; Zhang, Shuhua ; Azari, Hossein
Finite element analysis for a regularized variational inequality of the second kind. (English). In: Brandts, J., Chleboun, J., Korotov, S., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Applications of Mathematics 2012, In honor of the 60th birthday of Michal Křížek. Proceedings. Prague, May 2-5, 2012. Institute of Mathematics AS CR, Prague, 2012. pp. 317-331
MSC: 49J40, 49M25, 65K15, 65N12, 65N15, 65N30 | MR 3204423 | Zbl 1313.65176
Keywords:
finite element approximation; a priori error estimates; a posteriori error estimates; numerical examples; variational inequality; stability
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.
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