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A Stabilizer Free Weak Galerkin Finite Element Method for Brinkman Equations

A Stabilizer Free Weak Galerkin Finite Element Method for Brinkman Equations

Year:    2025

Author:    Haoning Dang, Qilong Zhai, Ran Zhang, Hui Peng

Journal of Computational Mathematics, Vol. 43 (2025), Iss. 1 : pp. 1–17

Abstract

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 $L^2$ 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.2307-m2022-0264

Journal of Computational Mathematics, Vol. 43 (2025), Iss. 1 : pp. 1–17

Published online:    2025-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Brinkman equations Weak Galerkin method Stabilizer free Discrete weak differential operators.

Author Details

Haoning Dang

Qilong Zhai

Ran Zhang

Hui Peng

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    https://doi.org/10.1063/5.0218131 [Citations: 0]