A stabilizer-free weak Galerkin finite element method on polytopal meshes

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:371

Article

Ye, Xiu¹  Zhang, Shangyou² 

[1] Univ Arkansas, Dept Math, Little Rock, AR 72204 USA

[2] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

关键词: Weak Galerkin;    Finite element methods;    Weak gradient;    Second-order elliptic problems;    Polyhedral meshes;   

DOI  :  10.1016/j.cam.2019.112699

来源: Elsevier

【 摘 要 】

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 Galerkin finite element methods will simplify formulations and reduce programming complexity significantly. The goal of this paper is to introduce a stabilizer free weak Galerkin (WG) finite element method for second order elliptic equations on polytopal meshes. This new WG method keeps a simple symmetric positive definite form and can work on polygonal polyhedral meshes. Optimal order error estimates are established for the corresponding WG approximations in both a discrete H-1 norm and the L-2 norm. Numerical results are presented verifying the theorem. Published by Elsevier B.V.

【 授权许可】

Free