The lowest-order stabilizer free weak Galerkin finite element method

摘要

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.