Journal of Nonlinear and Variational Analysis

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DOI: 10.23952/jnva.6.2022.5.06

Volume 6, Issue 5, 1 October 2022, Pages 517-534

 

Abstract. This paper is devoted to the numerical analysis of a general elliptic variational-hemivariational inequality. After a review of a solution existence and uniqueness result, we introduce a family of Galerkin methods to solve the problem. We prove the convergence of the numerical method under the minimal solution regularity condition available from the existence result and derive a Céa’s inequality for error estimation of the numerical solutions. Then, we apply the results for the numerical analysis of a variational-hemivariational inequality in the study of a static problem which models the contact of an elastic body with a reactive foundation. In particular, under appropriate solution regularity conditions, we derive an optimal order error estimate for the linear finite element solution.

 

How to Cite this Article:
Weimin Han, Mircea Sofonea, Numerical analysis of a general elliptic variational-hemivariational inequality, J. Nonlinear Var. Anal. 6 (2022), 517-534.