The lowest-order stabilizer free Weak Galerkin Finite Element Method

2020/04/01 by Ahmed Al‐Taweel, Xiaoshen Wang, Al-Taweel, Ahmed +1
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2004.00693

openalex publication_date 2020/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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≥ j₀ for some j₀, 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 \citeal2019note, the optimal of such j₀ 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.

Related

• A note on the optimal degree of the weak gradient of the stabilizer free weak Galerkin finite element method
• A new weak gradient for the stabilizer free weak Galerkin method with polynomial reduction
• A Weak Galerkin Finite Element Method with Polynomial Reduction
• A stabilizer free weak Galerkin finite element method on polytopal mesh: Part III
• A stabilizer free weak Galerkin element method with supercloseness of order two