Numerical analysis of stationary variational-hemivariational inequalities with applications in contact mechanics

This paper is devoted to numerical analysis of general finite element approximations to stationary variational-hemivariational inequalities with or without constraints. The focus is on convergence under minimal solution regularity and error estimation under suitable solution regularity assumptions that cover both internal and external approximations of the stationary variational-hemivariational inequalities. A framework is developed for general variational-hemivariational inequalities, including a convergence result and a Cea type inequality. It is illustrated how to derive optimal order error estimates for linear finite element solutions of sample problems from contact mechanics.