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 $L^{infty}(H^1)$ and $L^{infty}(L^2)$ norms are established for lowest order WG finite element space $({cal P}_{k}(K),;{cal P}_{k-1}(partial K),;big[{cal P}_{k-1}(K)big]^2)$. Finally, we give numerical examples to verify the theoretical results.