On the Finite Element Method for Mixed Variational Inequalities Arising in Elastoplasticity

We analyze the nite 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 elastoplastic problems are special cases, has been previously introduced and analyzed 31], and existence and uniqueness results for this problem have been given there. In this contribution the same approach is taken; that is, nite element approximations of the abstract variational inequality are analyzed, and the results are then discussed in further detail in the context of the concrete problems. Results on convergence are presented, as are error estimates. Regularization methods are commonly employed in variational inequalities of this kind, in both theoretical as well as computational investigations. We derive a-posteriori error estimates which enable us to determine whether the solution of a regularized problem can be taken as a suuciently accurate approximation of the solution of the original problem.