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

A systematic numerical study on weak Galerkin (WG) finite element method for second order linear parabolic problems is presented by allowing polynomial approximations with various degrees each local element. Convergence of both semidiscrete and fully discrete WG solutions are established in $L^{\infty}(L^2)$ $L^{\infty}(H^1)$ norms a general $({\cal P}_{k}(K),\;{\cal P}_{j}(\partial K),\;\big[{\cal P}_{l}(K)\big]^2)$, where $k\ge 1$, $j\ge 0$ $l\ge arbitrary integers. The space-time discretization based first time Euler scheme. Our results intended to extend the analysis methods elliptic [J. Sci. Comput., 74 (2018), 1369-1396] problems. Numerical experiments reported justify robustness, reliability accuracy method.