A modified weak Galerkin finite element method for a class of parabolic problems

In this paper, we consider the solution of parabolic equation using the modified weak Galerkin finite element procedure, which is named as MWG-FEM, based on the conception of the modified weak derivative over discontinuous functions with heterogeneous properties, in which the classical gradient operator is replaced by a modified weak gradient operator. Optimal order error estimates in a discrete L2 norm and H1 norm are established for the corresponding modified weak Galerkin finite element solutions. Finally, we numerically verify the convergence theory for the MWG-FEM through some examples.