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.

中文翻译：

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Stokes方程的压力鲁棒性交错不连续Galerkin方法

在本文中，我们通过使用分段常数近似为一般多边形网格上的斯托克斯方程提出了一种压力鲁棒性交错不连续伽辽金方法。我们通过利用发散保持速度重建算子修改离散公式中体力的右侧，这是压力无关速度误差估计的关键。证明了速度梯度、速度和压力的最优收敛。此外，通过在对偶问题中加入保散速度重构算子，我们能够证明速度逼近的超收敛性，这也是本文的一个重要贡献。最后，进行了一些数值实验以证实理论发现。