论文标题
无稳定剂，稳健和超偏弱的弱卷素有限元方法
A stabilizer free, pressure robust, and superconvergence weak Galerkin finite element method for the Stokes Equations on polytopal mesh
论文作者
论文摘要
在本文中，我们提出了一种新的无稳定剂和压力鲁棒的WG方法，用于在一级速度压力公式中具有超级连接的Stokes方程。在我们建议的方案中证明了收敛速率高于能量总和$ l^2 $ norm速度和$ l^2 $ norm和压力的最佳速度的收敛率。 $ h $（DIV） - 保证运算符是基于任意多项式学位的多边形网格构建的，并在身体源组装中使用，以打破经典离散化中质量保护不佳而引起的锁定现象。此外，我们提出的方案中的速度误差被证明与压力无关，从而确认了压力强度。对于Stokes模拟，我们提出的方案仅修饰人体源组装，但保持相同的刚度矩阵。进行了四个数值实验，以验证收敛结果和鲁棒性。
In this paper, we propose a new stabilizer free and pressure robust WG method for the Stokes equations with super-convergence on polytopal mesh in the primary velocity-pressure formulation. Convergence rates with one order higher than the optimal-order for velocity in both energy-norm and the $L^2$-norm and for pressure in $L^2$-norm are proved in our proposed scheme. The $H$(div)-preserving operator has been constructed based on the polygonal mesh for arbitrary polynomial degrees and employed in the body source assembling to break the locking phenomenon induced by poor mass conservation in the classical discretization. Moreover, the velocity error in our proposed scheme is proved to be independent of pressure and thus confirm the pressure-robustness. For Stokes simulation, our proposed scheme only modifies the body source assembling but remains the same stiffness matrix. Four numerical experiments are conducted to validate the convergence results and robustness.
