On the convergence of an explicit difference scheme for evolution variational inequalities with nonlocal space operator

Abstract

A nonlinear parabolic variational inequality with nonlocal space operator monotone with respect to gradient is considered. An explicit difference scheme with respect to the space operator and an implicit difference scheme with respect to the penalty operator are constructed by using the penalty method and the method of integral identities. Stability conditions for the constructed difference scheme are obtained. A convergence theorem with minimal assumptions on the smoothness of the initial data is proved.