On stabilizer-free weak Galerkin finite element methods on polytopal meshes

2019/06/16 by Xiu Ye, Ye, Xiu, Shangyou Zhang +1 · 3 citations
Engineering · #Advanced Numerical Methods in Computational Mathematics #Numerical methods in engineering #Electromagnetic Simulation and Numerical Methods

paper · pdf · doi:10.48550/arxiv.1906.06634

Abstract

A stabilizing/penalty term is often used in finite element methods with discontinuous approximations to enforce connection of discontinuous functions across element boundaries. Removing stabilizers from discontinuous finite element methods will simplify the formulations and reduce programming complexity significantly. The goal of this paper is to introduce a stabilizer free weak Galerkin finite element method for second order elliptic equations on polytopal meshes in 2D or 3D. This new WG method keeps a simple symmetric positive definite form and can work on polygonal/polyheral meshes. Optimal order error estimates are established for the corresponding WG approximations in both a discrete H¹ norm and the L² norm. Numerical results are presented verifying the theorem.

Citations

• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems

Cited by

• A stabilizer free weak Galerkin element method with supercloseness of order two
• A new weak gradient for the stabilizer free weak Galerkin method with polynomial reduction
• A stabilizer free weak Galerkin finite element method on polytopal mesh: Part II

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