A time-explicit weak Galerkin scheme for parabolic equations on polytopal partitions

Abstract In this paper a time-explicit weak Galerkin finite element method is introduced and analyzed for parabolic equations. The main idea relies on the inclusion of a stabilization term in the temporal direction in addition to the usual static stabilization in the weak Galerkin framework. Both semi-discrete and fully-discrete schemes in time are presented, as well as their stability and error analysis. Numerical results are reported for this new explicit weak Galerkin finite element method.