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