The lowest-order stabilizer free Weak Galerkin Finite Element Method

04/01/2020

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by   Ahmed Al-Taweel, et al.

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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 <cit.>, the optimal of such j_0 for certain types 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 2 D with the optimal order of convergence.