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This paper presents a general convergence theory of penalty based numerical methods for elliptic constrained inequality problems, including variational inequalities, hemivariational inequalities, and variational–hemivariational inequalities. The constraint is relaxed by a penalty formulation and is re-stored as the penalty parameter tends to zero. The main theoretical result of the paper is the convergence...
Variational-hemivariational inequalities refer to the inequality problems where both convex and nonconvex functions are involved. In this paper, we consider the numerical solution of a family of stationary variational-hemivariational inequalities by the finite element method. For a variational-hemivariational inequality of a general form, we prove convergence of numerical solutions. For some particular...
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