论文标题
压力强大的交错不连续的Galerkin方法用于Stokes方程
A pressure robust staggered discontinuous Galerkin method for the Stokes equations
论文作者
论文摘要
在本文中，我们提出了一种使用分段常数近似值的压力鲁棒交错的不连续的盖尔金方法，用于一般多边形网格上的stokes方程。我们通过利用差异保护速度重建操作员来修改离散配方中的右手，这是压力无关速度误差估计值的关键。证明了速度梯度，速度和压力的最佳收敛性。此外，我们能够通过将差异保留速度重建算子纳入双重问题来证明速度近似的超股，这也是本文的重要贡献。最后，进行了几项数值实验以确认理论发现。
In this paper we propose a pressure robust staggered discontinuous Galerkin method for the Stokes equations on general polygonal meshes by using piecewise constant approximations. We modify the right hand side of the body force in the discrete formulation by exploiting divergence preserving velocity reconstruction operator, which is the crux for pressure independent velocity error estimates. The optimal convergence for velocity gradient, velocity and pressure are proved. In addition, we are able to prove the superconvergence of velocity approximation by the incorporation of divergence preserving velocity reconstruction operator in the dual problem, which is also an important contribution of this paper. Finally, several numerical experiments are carried out to confirm the theoretical findings.
