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Volume 37, Issue 4
Numerical Analysis of Elliptic Hemivariational Inequalities for Semipermeable Media

Weimin Han, Ziping Huang, Cheng Wang & Wei Xu

DOI: 10.4208/jcm.1807-m2018-0035

J. Comp. Math., 37 (2019), pp. 506-523.

Published online: 2019-02

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  • Abstract

In this paper, we consider elliptic hemivariational inequalities arising in applications in semipermeable media. In its general form, the model includes both interior and boundary semipermeability terms. Detailed study is given on the hemivariational inequality in the case of isotropic and homogeneous semipermeable media. Solution existence and uniqueness of the problem are explored. Convergence of the Galerkin method is shown under the basic solution regularity available from the existence result. An optimal order error estimate is derived for the linear finite element solution under suitable solution regularity assumptions. The results can be readily extended to the study of more general hemivariational inequalities for non-isotropic and heterogeneous semipermeable media with interior semipermeability and/or boundary semipermeability. Numerical examples are presented to show the performance of the finite element approximations; in particular, the theoretically predicted optimal first order convergence in $H^1$ norm of the linear element solutions is clearly observed.

  • Keywords

Hemivariational inequality, interior semipermeability, boundary semipermeability, finite element method, error estimate.

  • AMS Subject Headings

65N30, 49J40

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

weimin-han@uiowa.edu (Weimin Han)

huangziping@tongji.edu.cn (Ziping Huang)

cwang1@umassd.edu (Cheng Wang)

xuwei820824@163.com (Wei Xu)

  • BibTex
  • RIS
  • TXT
@Article{JCM-37-506, author = {Han , WeiminHuang , ZipingWang , Cheng and Xu , Wei}, title = {Numerical Analysis of Elliptic Hemivariational Inequalities for Semipermeable Media}, journal = {Journal of Computational Mathematics}, year = {2019}, volume = {37}, number = {4}, pages = {506--523}, abstract = {

In this paper, we consider elliptic hemivariational inequalities arising in applications in semipermeable media. In its general form, the model includes both interior and boundary semipermeability terms. Detailed study is given on the hemivariational inequality in the case of isotropic and homogeneous semipermeable media. Solution existence and uniqueness of the problem are explored. Convergence of the Galerkin method is shown under the basic solution regularity available from the existence result. An optimal order error estimate is derived for the linear finite element solution under suitable solution regularity assumptions. The results can be readily extended to the study of more general hemivariational inequalities for non-isotropic and heterogeneous semipermeable media with interior semipermeability and/or boundary semipermeability. Numerical examples are presented to show the performance of the finite element approximations; in particular, the theoretically predicted optimal first order convergence in $H^1$ norm of the linear element solutions is clearly observed.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1807-m2018-0035}, url = {http://global-sci.org/intro/article_detail/jcm/13006.html} }
TY - JOUR T1 - Numerical Analysis of Elliptic Hemivariational Inequalities for Semipermeable Media AU - Han , Weimin AU - Huang , Ziping AU - Wang , Cheng AU - Xu , Wei JO - Journal of Computational Mathematics VL - 4 SP - 506 EP - 523 PY - 2019 DA - 2019/02 SN - 37 DO - http://doi.org/10.4208/jcm.1807-m2018-0035 UR - https://global-sci.org/intro/article_detail/jcm/13006.html KW - Hemivariational inequality, interior semipermeability, boundary semipermeability, finite element method, error estimate. AB -

In this paper, we consider elliptic hemivariational inequalities arising in applications in semipermeable media. In its general form, the model includes both interior and boundary semipermeability terms. Detailed study is given on the hemivariational inequality in the case of isotropic and homogeneous semipermeable media. Solution existence and uniqueness of the problem are explored. Convergence of the Galerkin method is shown under the basic solution regularity available from the existence result. An optimal order error estimate is derived for the linear finite element solution under suitable solution regularity assumptions. The results can be readily extended to the study of more general hemivariational inequalities for non-isotropic and heterogeneous semipermeable media with interior semipermeability and/or boundary semipermeability. Numerical examples are presented to show the performance of the finite element approximations; in particular, the theoretically predicted optimal first order convergence in $H^1$ norm of the linear element solutions is clearly observed.

Han , WeiminHuang , ZipingWang , Cheng and Xu , Wei. (2019). Numerical Analysis of Elliptic Hemivariational Inequalities for Semipermeable Media. Journal of Computational Mathematics. 37 (4). 506-523. doi:10.4208/jcm.1807-m2018-0035
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