A Stabilizer Free Weak Galerkin Finite Element Method for Brinkman Equations (Journal of Computational Mathematics, 2024)
We develop a stabilizer free weak Galerkin (SFWG) finite element method for Brinkmanequations. The main idea is to use high order polynomials to compute the discrete weakgradient and then the stabilizing term is removed from the numerical formulation. TheSFWG scheme is very simple and easy to implement on polygonal meshes. We provethe 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 SFWGmethod 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 SFWGmethod.
Keywords: Brinkman equations; Weak Galerkin method; Stabilizer free; Discrete weak differential operators.