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This paper is devoted to a study of the numerical solution of elliptic hemivariational inequalities with or without convex constraints by the finite element method. For a general family of elliptic...

We study discontinuous Galerkin methods for solving elliptic variational inequalities of both the first and second kinds. Analysis of numerous discontinuous Galerkin schemes for elliptic boundary value problems is extended to the variational inequalities. We establish a priori error estimates for the discontinuous Galerkin methods, which reach optimal order for linear elements. Results from some numerical examples are reported.

In this paper we analyze nonconforming finite element methods for solving a fourth order elliptic variational inequality of the second kind arising in a plate frictional contact problem. The variational inequality involves a nondifferentiable term due to the frictional contact. Optimal order error estimates are derived for both continuous and discontinuous nonconforming finite elements.

We consider numerical approximations of a class of abstract nonlinear evolutionary systems arising in the study of quasi-static frictional contact problems for elastic-viscoplastic materials. Both semidiscrete and fully discrete schemes are analyzed. Strong convergence of both approximations is established under minimal solution regularity. The results are applied to two particular frictional contact problems for viscoplastic bodies, where the finite element method is employed to discretize the spatial domain. Under additional regularity assumptions on the exact solution, some error estimates are derived.

We consider a class of evolutionary variational inequalities arising in various frictional contact problems for viscoelastic materials. Under the smallness assumption of a certain coefficient, we prove an existence and uniqueness result using Banach's fixed point theorem. We then study two numerical approximation schemes of the problem: a semidiscrete scheme and a fully discrete scheme. For both schemes, we show the existence of a unique solution and derive error estimates. Finally, all these results are applied to the analysis and numerical approximations of a viscoelastic frictional contact problem, with the finite element method used to discretize the spatial domain.

We analyze the finite-element method for a class of mixed variational inequalities of the second kind, which arises in elastoplastic problems. An abstract variational inequality, of which the elast...