A New Weak Galerkin Finite Element Scheme for the Brinkman Model (Communications in Computational Physics, 2020)
The Brinkman model describes flow of fluid in complex porous media witha high-contrast permeability coefficient such that the flow is dominated by Darcy insome regions and by Stokes in others. A weak Galerkin (WG) finite element methodfor solving the Brinkman equations in two or three dimensional spaces by using polynomialsis developed and analyzed. The WG method is designed by using the generalizedfunctions and their weak derivatives which are defined as generalized distributions.The variational form we considered in this paper is based on two gradient operatorswhich is different from the usual gradient-divergence operators for Brinkmanequations. The WG method is highly flexible by allowing the use of discontinuousfunctions on arbitrary polygons or polyhedra with certain shape regularity. Optimal-ordererror estimates are established for the corresponding WG finite element solutionsin various norms. Some computational results are presented to demonstrate therobustness, reliability, accuracy, and flexibility of the WG method for the Brinkmanequations.