Robust weak Galerkin finite element solvers for Stokes flow based on a lifting operator
Robust weak Galerkin finite element solvers for Stokes flow based on a lifting operator
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DOI：
10.1016/j.camwa.2022.08.043
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发表时间：
2022-11
期刊：
影响因子：
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通讯作者：
Zhuoran Wang;Ruishu Wang;Jiangguo Liu
中科院分区：
文献类型：
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作者：
Zhuoran Wang;Ruishu Wang;Jiangguo Liu
本文提出了新的有限元求解斯托克斯流的压力鲁棒性，由于使用了提升算子。具体地说，弱伽辽金（WG）有限元格式开发的Stokes问题的四边形和六面体网格。局部Arbogast-Correa或Arbogast-Tao空间用于构造离散弱梯度。提升算子将WG测试函数提升到H（div）子空间中，并消除速度误差对压力的依赖性。这些求解器的压力鲁棒性进行了理论验证和数值说明。与非鲁棒的经典泰勒-胡德（Q2，Q1）求解器的比较。
This paper presents novel finite element solvers for Stokes flow that are pressure-robust due to the use of a lifting operator. Specifically, weak Galerkin (WG) finite element schemes are developed for the Stokes problem on quadrilateral and hexahedral meshes. Local Arbogast-Correa or Arbogast-Tao spaces are utilized for construction of discrete weak gradients. The lifting operator lifts WG test functions into H (div)-subspaces and removes pressure dependence of velocity errors. The pressure robustness of these solvers is validated theoretically and illustrated numerically. Comparison with the non-robust classical Taylor-Hood (Q 2, Q 1) solver is presented.