A systematic study on weak Galerkin finite element method for second-order parabolic problems

In the present work, we have described a systematic numerical study on weak Galerkin (WG) finite element method for second-order linear parabolic problems by allowing polynomial approximations with various degrees for each local element. Convergence of both semidiscrete and fully discrete WG solutions are established in L infinity (L2) and L infinity (H1) norms for a general WG element (Pk(K), Pj(??????K), [Pl(K)]2), where k > 1, j > 0 and l > 0 are arbitrary integers. The fully discrete space-time discretization is based on a first order in time Euler scheme. Numerical experiments are reported to justify the robustness, reliability and accuracy of the WG finite element method.