Hybridized Weak Galerkin Finite Element Methods For The Brinkman Equations

This paper introduces a numerical method for solving Brinkman equation-hy-bridized weak Galerkin finite element method,which is short for HWG method.On the one hand,the hybridized weak Galerkin finite element method remains the key idea of the WG method,introducing the weak differential operators for the discontinuous weak functions.On the other hand,the method is able to lower the requirement of bound-ary continuity by introducing Lagrange multiplier.In this paper,we consider the HWG method for Brinkman equation with three kinds of boundary conditions,at the same time,the well-posedness of numerical format are proved,and further we achieve the optimal error estimates of the energy norm and L2 norm respectively.A Schur complement for-mulation is derived to reduce the computational complexity.In the end,some numerical examples are given to verify the effectiveness of the algorithms.