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 - <p style="text-align: justify;">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.</p>