Randomized trial demonstrates stability and accuracy of a stabilizer-free method for nonconvex geometries, suggesting improved computational efficiency.
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.
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Wang et al. (2026) studied this question.
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