SIAM Journal on Scientific Computing, Volume 42, Issue 3, Page B608-B629, January 2020.
In this paper, we develop a pressure robust weak Galerkin finite element scheme for Stokes equations on polygonal mesh. The major idea for achieving a pressure-independent energy-error estimate is to use a divergence preserving velocity reconstruction operator in the discretization of the right-hand side body force. Our scheme only modifies the body force assembling but remains the same stiffness matrix for Stokes simulation. The optimal convergence results for velocity and pressure have been established in this paper. Finally, numerical examples based on triangular, rectangular, and polygonal meshes are presented for validating the theoretical conclusions.

中文翻译：

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斯托克斯问题的压力鲁棒弱Galerkin有限元方法

SIAM科学计算杂志，第42卷，第3期，第B608-B629页，2020
年1月。在本文中，我们为多边形网格上的Stokes方程开发了一种压力鲁棒的弱Galerkin有限元方案。实现压力无关的能量误差估计的主要思想是在离散右侧力时使用发散保持速度重构算子。我们的方案仅修改了车身力的装配，但对于Stokes仿真而言，其刚度矩阵保持不变。建立了速度和压力的最优收敛结果。最后，给出了基于三角形，矩形和多边形网格的数值示例，以验证理论结论。