A divergence free weak virtual element method for the Stokes-Darcy problem on general meshes
A divergence free weak virtual element method for the Stokes-Darcy problem on general meshes
复制标题
求解一般网格Stokes-Darcy问题的无散弱虚元法
DOI：
10.1016/j.cma.2018.10.022
复制
发表时间：
2019
影响因子：
7.2
通讯作者：
He Yinnian
中科院分区：
文献类型：
--
作者：
Wang Gang;Wang Feng;Chen Long;He Yinnian
本文提出了一种在一般网格上求解具有Beavers-Joseph-Saffman界面条件的Stokes-Darcy问题的弱虚元方法。速度由H（div）虚拟元素离散化。压力用不连续的分段多项式近似。此外，在单元面上引入了一个多项式空间来近似Stokes方程中的切向速度迹线。离散水平上的速度是完全发散自由的，因此在离散中保持了精确的质量守恒。证明了离散问题的适定性，并推导出一个先验误差估计，这意味着在适当的范数下速度的误差不依赖于压力。一系列的数值实验报告，以说明该方法的性能。
This paper presents a weak virtual element method on general meshes for the Stokes–Darcy problem with the Beavers–Joseph–Saffman interface condition. The velocity is discretized by the H (div) virtual element. The pressure is approximated by discontinuous piecewise polynomials. Besides, a polynomial space on the element faces is introduced to approximate the tangential trace of the velocity in the Stokes equations. The velocity on the discrete level is exactly divergence free and thus the exact mass conservation is preserved in the discretization. The well-posedness of the discrete problem is proved and an a priori error estimate is derived that implies the error for the velocity in a suitable norm does not depend on the pressure. A series of numerical experiments are reported to illustrate the performance of the method.