A STABILIZER FREE WEAK GALERKIN FINITE ELEMENT METHOD FOR BRINKMAN EQUATIONS  

作　　者：Haoning Dang Qilong Zhai Ran Zhang Hui Peng 

机构地区：[1]School of Mathematics,Jilin University,Changchun 130012,China [2]School of Mathematical Sciences and MOE-LSC,Shanghai Jiao Tong University,Shanghai 200240,China

出　　处：《Journal of Computational Mathematics》2025年第1期1-17,共17页计算数学(英文)

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.1901015,12271208,11971198,91630201,11871245,11771179,11826101);by the Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education,Jilin University.

摘　　要：We develop a stabilizer free weak Galerkin (SFWG) finite element method for Brinkman equations. The main idea is to use high order polynomials to compute the discrete weak gradient and then the stabilizing term is removed from the numerical formulation. The SFWG scheme is very simple and easy to implement on polygonal meshes. We prove the well-posedness of the scheme and derive optimal order error estimates in energy and L2 norm. The error results are independent of the permeability tensor, hence the SFWG method is stable and accurate for both the Stokes and Darcy dominated problems. Finally, we present some numerical experiments to verify the efficiency and stability of the SFWG method.

关 键 词：Brinkman equations Weak Galerkin method Stabilizer free Discrete weak differential operators 

分 类 号：O17[理学—数学]