论文标题
重建操作员，用于Stokes问题的压力刺激性嵌入式不连续的Galerkin方法
A pressure-robust embedded discontinuous Galerkin method for the Stokes problem by reconstruction operators
论文作者
论文摘要
用于Stokes问题的嵌入式不连续的Galerkin（EDG）有限元方法导致细胞上无点的无分差近似速度。但是，近似速度不是h（div）符合性的，可以证明这是EDG方法不是压力稳定的原因，即速度的误差取决于连续压力。在本文中，我们提出了一个本地重建操作员，该操作员将无差异测试功能映射到完全无差异测试功能。该局部重建操作员仅通过更改离散化的右侧来恢复压力量，类似于Lederer等人最近针对Taylor-Hood和Mini Elements引入的重建运算符。 （Siam J.Numer。Anal。，55（2017），第1291---1314页）。我们对离散化的先验误差分析，显示速度误差的最佳收敛速率和压力稳定性。这些结果通过数值示例验证。这项研究的动机是，由此产生的EDG方法将不连续的盖尔金方法的多功能性与连续盖尔金方法的计算效率以及压力射击有限元方法的准确性相结合。
The embedded discontinuous Galerkin (EDG) finite element method for the Stokes problem results in a point-wise divergence-free approximate velocity on cells. However, the approximate velocity is not H(div)-conforming and it can be shown that this is the reason that the EDG method is not pressure-robust, i.e., the error in the velocity depends on the continuous pressure. In this paper we present a local reconstruction operator that maps discretely divergence-free test functions to exactly divergence-free test functions. This local reconstruction operator restores pressure-robustness by only changing the right hand side of the discretization, similar to the reconstruction operator recently introduced for the Taylor--Hood and mini elements by Lederer et al. (SIAM J. Numer. Anal., 55 (2017), pp. 1291--1314). We present an a priori error analysis of the discretization showing optimal convergence rates and pressure-robustness of the velocity error. These results are verified by numerical examples. The motivation for this research is that the resulting EDG method combines the versatility of discontinuous Galerkin methods with the computational efficiency of continuous Galerkin methods and accuracy of pressure-robust finite element methods.
