TY - JOUR
T1 - A Stabilizer Free Weak Galerkin Finite Element Method for Brinkman Equations
AU - Dang , Haoning
AU - Zhai , Qilong
AU - Zhang , Ran
AU - Peng , Hui
JO - Journal of Computational Mathematics
VL - 1
SP - 1
EP - 17
PY - 2024
DA - 2024/11
SN - 43
DO - http://doi.org/10.4208/jcm.2307-m2022-0264
UR - https://global-sci.org/intro/article_detail/jcm/23527.html
KW - Brinkman equations, Weak Galerkin method, Stabilizer free, Discrete weak
differential operators.
AB - <p style="text-align: justify;">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.</p>