A Simple Weak Galerkin Method for the Brinkman Equations on Nonconvex Polytopal Meshes

ABSTRACT This paper presents a stabilizer‐free weak Galerkin (WG) finite element method for the Brinkman equations that eliminates the need for conventional stabilization techniques. The proposed WG method accommodates general finite element partitions consisting of both convex and nonconvex polytopal elements. Bubble functions are employed as a key analytical component to ensure stability and convergence. Optimal‐order error estimates are rigorously derived for the WG finite element solutions. A series of numerical experiments is conducted to validate the theoretical results.