Before revision:  Finally, a numerical study is done based on P_1-finite element approximation for space discretization and implicit Euler scheme for time discretization , where we study the stability of the scheme, analysis of the error and obtained some numerical simulations  .
After revision:  Finally, a numerical study is done based on P_1-finite element approximation for space discretization and implicit Euler scheme for time discretization . Then, we showed that the discrete energy decays, later a priori error estimates are established. Finally , some numerical simulations .