Finite element analysis for a regularized variational inequality of the second kind

Zhang, Tie, Zhang, Shuhua, and Azari, Hossein. "Finite element analysis for a regularized variational inequality of the second kind." Applications of Mathematics 2012. Prague: Institute of Mathematics AS CR, 2012. 317-331. <http://eudml.org/doc/287802>.

@inProceedings{Zhang2012,
abstract = {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.},
author = {Zhang, Tie, Zhang, Shuhua, Azari, Hossein},
booktitle = {Applications of Mathematics 2012},
keywords = {finite element approximation; a priori error estimates; a posteriori error estimates; numerical examples; variational inequality; stability},
location = {Prague},
pages = {317-331},
publisher = {Institute of Mathematics AS CR},
title = {Finite element analysis for a regularized variational inequality of the second kind},
url = {http://eudml.org/doc/287802},
year = {2012},
}

TY - CLSWK
AU - Zhang, Tie
AU - Zhang, Shuhua
AU - Azari, Hossein
TI - Finite element analysis for a regularized variational inequality of the second kind
T2 - Applications of Mathematics 2012
PY - 2012
CY - Prague
PB - Institute of Mathematics AS CR
SP - 317
EP - 331
AB - 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.
KW - finite element approximation; a priori error estimates; a posteriori error estimates; numerical examples; variational inequality; stability
UR - http://eudml.org/doc/287802
ER -