Convergence Analysis Of Time Discontinuous Galerkin Finite Element Solution For General Parabolic Equation

A fully-discrete space-time discontinuous finite element procedure, continuous in space but discontinuous in time, for a, kind of genera.l parabolic equation is studied. The optimal-order error estimate in L∞(L2)-norm is proved by using the techniques of combining finite difference and finite element method. Moreover, the optimal-order error estimate in L∞(H1)-norm is derived under some assumptions on space-time meshes. Finally, numerical results are presented to confirm the theoretical results...