论文标题
各向异性弱化力过度的对称内部惩罚方法
Anisotropic weakly over-penalised symmetric interior penalty method for the Stokes equation
论文作者
论文摘要
在这项研究中，我们研究了一种各向异性弱的过度覆盖的对称内部惩罚方法，用于stokes方程{convex域}。我们的方法是一种简单的不连续的Galerkin方法，类似于Crouzeix--raviart有限元方法。作为我们的主要贡献，我们为一致性项展示了一个新的证明，这使我们能够获得各向异性一致性误差的估计。证明的关键思想是应用raviart - thomas有限元空间与不连续空间之间的关系。尽管已经广泛讨论了不连续的盖尔金方法的Inf-SUP稳定方案，但我们的结果表明，Stokes元素满足各向异性网格上的Inf-Sup条件。此外，我们在各向异性网格上提供了能量规范中的误差估计。在数值实验中，我们比较了标准和各向异性网状分区的计算结果。
In this study, we investigate an anisotropic weakly over-penalised symmetric interior penalty method for the Stokes equation {on convex domains}. Our approach is a simple discontinuous Galerkin method similar to the Crouzeix--Raviart finite element method. As our primary contribution, we show a new proof for the consistency term, which allows us to obtain an estimate of the anisotropic consistency error. The key idea of the proof is to apply the relation between the Raviart--Thomas finite element space and a discontinuous space. While inf-sup stable schemes of the discontinuous Galerkin method on shape-regular mesh partitions have been widely discussed, our results show that the Stokes element satisfies the inf-sup condition on anisotropic meshes. Furthermore, we provide an error estimate in an energy norm on anisotropic meshes. In numerical experiments, we compare calculation results for standard and anisotropic mesh partitions.
