WEAK GALERKIN FINITE ELEMENT METHODS COMBINED WITH CRANK-NICOLSON SCHEME FOR PARABOLIC INTERFACE PROBLEMS

This article is devoted to the a priori error estimates of the fully discrete Crank-Nicolson approximation for the linear parabolic interface problem via weak Galerkin finite element methods (WG-FEM). All the finite element functions are discontinuous for which the usual gradient operator is implemented as distributions in properly defined spaces. Optimal order error estimates in both L-infinity (H-1) and L-infinity (L-2) norms are established for lowest order WG finite element space (P-k(K), Pk-1(partial derivative K), [Pk-1(K)](2)). Finally, we give numerical examples to verify the theoretical results.