The lowest-order stabilizer free weak Galerkin finite element method

Recently, a new stabilizer free weak Galerkin method (SFWG) is proposed, which is easier to implement and more efficient. The main idea is that by letting j >= j(0) for some j(0), where j is the degree of the polynomials used to compute the weak gradients, then the stabilizer term in the regular weak Galerkin method is no longer needed. Later on in [1], the optimal of such j(0) for a certain type of finite element spaces was given. In this paper, we propose a new efficient SFWG scheme using the lowest possible orders of piecewise polynomials for triangular meshes in 2D with the optimal order of convergence. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.