A posteriori error estimates of the weak Galerkin finite element methods for parabolic problems

In this paper, We propose the residual-based a posteriori error estimator of the weak Galerkin finite element method with the backward Euler time discretization for the linear parabolic partial differential equation. For the a posteriori error estimator, we introduce the Helmholtz decomposition technique to prove its reliability. We mainly study WG element (P-j(K),P-l(partial derivative K),V(K,r) = RTj(K)). Numerical experiments based on the lowest order case, i.e. (P-0(K),P-0(partial derivative K),RT0(K)), are provided to verify the theoretical research.