A stabilizer free weak Galerkin finite element method on polytopal mesh: Part II

A stabilizer free weak Galerkin (WG) finite element method on polytopal mesh has been introduced in Part I of this paper (Ye and Zhang (2020)). Removing stabilizers from discontinuous finite element methods simplifies formulations and reduces programming complexity. The purpose of this paper is to introduce a new WG method without stabilizers on polytopal mesh that has convergence rates one order higher than optimal convergence rates. This method is the first WG method that achieves superconvergence on polytopal mesh. Numerical examples in 2D and 3D are presented verifying the theorem. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This paper introduces a stabilizer free weak Galerkin finite element method on polytopal mesh with convergence rates one order higher than optimal convergence rates, achieving superconvergence on polytopal mesh. Numerical examples in 2D and 3D are presented to verify the theorem.