Before revision:  Energy identities and stability estimates of the discrete problem are proved for a slightly more general problem , that are used to prove optimal order a priori error estimates with minimal regularity requirement . Uniform norm in time error estimates are proved for the constant and linear cases . Numerical experiments are performed to verify the theoretical rate of convergence.
After revision:  Energy identities and stability estimates of the discrete problem are proved for a slightly more general problem , that are used to prove optimal order a priori error estimates with minimal regularity requirement on the solution. The combination with the classic continuous Galerkin finite element discretization in space variable is used, to formulate a full-discrete scheme. The a priori error analysis is presented . Numerical experiments are performed to verify the theoretical rate of convergence.