Convergence of a double step scheme for a class of parabolic Clarke subdifferential inclusions?

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