Hybridized weak Galerkin finite element methods for Brinkman equations

<p style='text-indent:20px;'>This paper presents a hybridized weak Galerkin (HWG) finite element method for solving the Brinkman equations. Mathematically, equations can model Stokes and Darcy flows in unified framework so as to describe fluid motion porous media with fractures. Numerical schemes equations, therefore, must be designed tackle at same time. We demonstrate that HWG is capable of providing very accurate stable numerical approximations both Stokes. The main features it approximates differential operators by their forms distributions introduces Lagrange multipliers relax certain constraints. establish optimal order error estimates solutions also present Schur complement formulation HWG, which reduces systems' computational complexity significantly. A number experiments are provided confirm theoretical developments.</p>