Numerical Analysis of Elliptic Hemivariational Inequalities for Semipermeable Media (Journal of Computational Mathematics, 2019)
In this paper, we consider elliptic hemivariational inequalities arising in applications insemipermeable media. In its general form, the model includes both interior and boundarysemipermeability terms. Detailed study is given on the hemivariational inequality in thecase of isotropic and homogeneous semipermeable media. Solution existence and uniqueness of the problem are explored. Convergence of the Galerkin method is shown underthe basic solution regularity available from the existence result. An optimal order errorestimate is derived for the linear finite element solution under suitable solution regularityassumptions. The results can be readily extended to the study of more general hemivariational inequalities for non-isotropic and heterogeneous semipermeable media with interiorsemipermeability and/or boundary semipermeability. Numerical examples are presentedto 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 solutionsis clearly observed.
Keywords: Hemivariational inequality; interior semipermeability; boundary semipermeability; finite element method; error estimate.