Discontinuous Galerkin Time Stepping for Semilinear Parabolic Problems with Time Constant Delay

In this paper, a discontinuous Galerkin (DG) time stepping method combined with the standard finite element method in space is proposed to solve a class of semilinear parabolic differential equations with time constant delay. The time semi-discretization and the relevant global convergence of the DG solution under suitable uniform meshes are derived. The standard Galerkin method in space is used to obtain the fully discrete scheme and the optimal global convergence of the full discretization is presented. Numerical experiments for one-dimensional and two-dimensional equations are provided to demonstrate the theoretical results.