  In this paper we deal with a second order evolution inclusion involving a
multivalued term generated by a Clarke subdifferential of a locally Lipschitz
potential. For this problem we construct a double step time-semidiscrete
approximation, known as the Rothe scheme. We study a sequence of solutions of
the semidiscrete approximate problems and provide its weak convergence to a
limit element that is a solution of the original problem.

Numerical Analysis;Numerical Analysis;Analysis of PDEs