Weak Galerkin mixed finite element method for heat equation

In this paper, we apply a new weak Galerkin mixed finite element method (WGMFEM) with stabilization term to solve heat equations. This method allows the usage of totally discontinuous functions in the approximation space. The WGMFEM is capable of providing very accurate numerical approximations for both the primary and flux variables. In addition, we develop and analyze the error estimates for both continuous and discontinuous time WGMFEM schemes. Optimal order error estimates in both L2 and triple-bar ⫼⋅⫼ norms are established, respectively. Finally, numerical tests are conducted to illustrate the theoretical results.