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Volume 14, Issue 3
The Virtual Element Method for an Elliptic Hemivariational Inequality with Convex Constraint

Fang Feng, Weimin Han & Jianguo Huang

Numer. Math. Theor. Meth. Appl., 14 (2021), pp. 589-612.

Published online: 2021-06

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  • Abstract

An abstract framework of numerical method is devised for solving an elliptic hemivariational inequality with convex constraint. Convergence of the method is explored under the minimal solution regularity available from the well-posedness of the hemivariational inequality. A Céa-type inequality is derived for error estimation. As a typical example, a virtual element method is proposed to solve a frictionless unilateral contact problem and its optimal error estimates are obtained as well. Numerical results are reported to show the performance of the proposed method.

  • AMS Subject Headings

65N30

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COPYRIGHT: © Global Science Press

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@Article{NMTMA-14-589, author = {Feng , FangHan , Weimin and Huang , Jianguo}, title = {The Virtual Element Method for an Elliptic Hemivariational Inequality with Convex Constraint}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2021}, volume = {14}, number = {3}, pages = {589--612}, abstract = {

An abstract framework of numerical method is devised for solving an elliptic hemivariational inequality with convex constraint. Convergence of the method is explored under the minimal solution regularity available from the well-posedness of the hemivariational inequality. A Céa-type inequality is derived for error estimation. As a typical example, a virtual element method is proposed to solve a frictionless unilateral contact problem and its optimal error estimates are obtained as well. Numerical results are reported to show the performance of the proposed method.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2020-0180}, url = {http://global-sci.org/intro/article_detail/nmtma/19190.html} }
TY - JOUR T1 - The Virtual Element Method for an Elliptic Hemivariational Inequality with Convex Constraint AU - Feng , Fang AU - Han , Weimin AU - Huang , Jianguo JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 589 EP - 612 PY - 2021 DA - 2021/06 SN - 14 DO - http://doi.org/10.4208/nmtma.OA-2020-0180 UR - https://global-sci.org/intro/article_detail/nmtma/19190.html KW - Virtual element method, hemivariational inequality, error estimate, multiobjective double bundle method. AB -

An abstract framework of numerical method is devised for solving an elliptic hemivariational inequality with convex constraint. Convergence of the method is explored under the minimal solution regularity available from the well-posedness of the hemivariational inequality. A Céa-type inequality is derived for error estimation. As a typical example, a virtual element method is proposed to solve a frictionless unilateral contact problem and its optimal error estimates are obtained as well. Numerical results are reported to show the performance of the proposed method.

Fang Feng, Weimin Han & Jianguo Huang. (2021). The Virtual Element Method for an Elliptic Hemivariational Inequality with Convex Constraint. Numerical Mathematics: Theory, Methods and Applications. 14 (3). 589-612. doi:10.4208/nmtma.OA-2020-0180
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