当前位置: X-MOL 学术Comput. Methods Appl. Mech. Eng. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
A pressure-robust virtual element method for the Stokes problem
Computer Methods in Applied Mechanics and Engineering ( IF 7.2 ) Pub Date : 2021-04-26 , DOI: 10.1016/j.cma.2021.113879
Gang Wang , Lin Mu , Ying Wang , Yinnian He

In this paper, we introduce a pressure-robust virtual element method for the Stokes problem on convex polygonal meshes. The method is based on the lowest order virtual element, in which the degrees of freedom for the velocity are simply given by the evaluations of velocity at the mesh vertices and the average values of normal velocity across the mesh edges, and the pressure is approximated by piecewise constants. In the standard virtual element scheme, an average of nodal values of test function is used in the approximation of right hand side to obtain the computability and achieve optimal approximation. However, such standard scheme involves a pressure contribution in the velocity error. To achieve the pressure-independent velocity approximation, we define an H(div)-conforming velocity reconstruction operator for the velocity test function and propose the modified scheme by employing it in the approximation of right-hand-side source term assembling. Compared with the standard scheme, the stiffness matrix keeps unchanged and only the approximation of the right hand side changes. The error estimates for the velocity and pressure have been proved, which imply that the velocity error is independent of pressure. Numerical experiments are shown to validate the theoretical conclusions.



中文翻译:

斯托克斯问题的压力稳健虚拟单元法

在本文中,我们针对凸多边形网格上的Stokes问题引入了一种压力稳健的虚拟单元法该方法基于最低阶虚拟元素,其中速度的自由度仅通过评估网格顶点处的速度和跨网格边缘的法向速度的平均值来简单给出,而压力近似为分段常数。在标准虚拟单元方案中,将测试函数的节点值的平均值用于右手侧的近似中,以获得可计算性并实现最佳近似。然而,这种标准方案涉及速度误差中的压力贡献。为了获得与压力无关的速度近似值,我们定义了H股利速度测试函数的符合速度重建算子,并通过在右侧源项组合的近似中应用修改方案来提出。与标准方案相比,刚度矩阵保持不变,仅右手侧的近似值发生变化。已经证明了速度和压力的误差估计,这意味着速度误差与压力无关。数值实验证明了理论结论的正确性。

更新日期:2021-04-26
down
wechat
bug