Inf–sup stability of isogeometric Taylor–Hood and Sub-Grid methods for the Stokes problem with hierarchical splines
Inf–sup stability of isogeometric Taylor–Hood and Sub-Grid methods for the Stokes problem with hierarchical splines
复制标题
具有分层样条的 Stokes 问题的等几何 Taylor-Hood 和子网格方法的 Inf-sup 稳定性
DOI：
10.1093/imanum/drx031
复制
发表时间：
2018
影响因子：
2.1
通讯作者：
B. Jüttler
中科院分区：
文献类型：
--
作者：
A. Bressan;B. Jüttler
在本文中，我们证明了Stokes问题的自适应等几何离散化的自支持稳定性。离散化是基于等高Taylor-Hood和Sub-Grid单元的分层泛化，这些单元由Bressan和Sangalli（2013）描述，Stokes问题的等高离散化：通过宏单元技术进行稳定性分析。IMA J.数字。分析的。计算张量-积样条曲线，vol . 33, 629-651)。为了将现有的证明扩展到层次设置，我们需要对一些步骤进行相当大的调整。特别地，通过分析Speleers & Manni （2016, Effortless quasi-interpolation In hierarchical space . number .）的准插值的性质，得到了所需的局部逼近估计。数学。，132, 155-184)关于某些Sobolev规范。除了理论结果外，我们还进行了数值试验，以分析网格规则性假设对inf-sup常数的依赖关系。最后，本文还对所得到的自适应方法在t形域上的收敛性进行了数值检验。
In this article, we prove the inf–sup stability of an adaptive isogeometric discretization of the Stokes problem. The discretization is based on the hierarchical generalization of the isogeometric Taylor–Hood and Sub-Grid elements, which were described by Bressan & Sangalli (2013, Isogeometric discretizations of the Stokes problem: stability analysis by the macroelement technique.IMA J. Numer. Anal.,33, 629–651) for tensor-product splines. In order to extend the existing proof to the hierarchical setting, we need to adapt some of the steps considerably. In particular, the required local approximation estimate is obtained by analysing the properties of the quasi-interpolant of Speleers & Manni (2016, Effortless quasi-interpolation in hierarchical spaces.Numer. Math.,132, 155–184) with respect to certain Sobolev norms.In addition to the theoretical results, we also perform numerical tests in order to analyse the dependency of the inf–sup constant on the mesh regularity assumptions. Finally, the article also presents a numerical convergence test of the resulting adaptive method on a T-shaped domain.
DOI：
10.1016/j.cma.2012.06.023
发表时间：
2013-01-01
影响因子：
7.2
作者：
Bornemann, P. B.;Cirak, F.
通讯作者：
Cirak, F.