# Article

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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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