Local projection FEM stabilization for the time‐dependent incompressible Navier–Stokes problem
Local projection FEM stabilization for the time‐dependent incompressible Navier–Stokes problem
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DOI：
10.1002/num.21944
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发表时间：
2015-07
影响因子：
3.9
通讯作者：
D. Arndt;Helene Dallmann;G. Lube
中科院分区：
文献类型：
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作者：
D. Arndt;Helene Dallmann;G. Lube
我们考虑时间相关的不可压缩Navier-Stokes问题的协调有限元（FE）近似，速度和压力的非超稳定近似。在高雷诺数情况下，考虑了局部投影稳定方法。特别是，流线迎风的思想与无发散约束的稳定性相结合。对于所产生的非线性半离散问题，给出了稳定性和收敛性分析。我们的方法改进了Matthies和Tobiska（IMA J. Numer.分析：出现）的线性化模型，并采取了部分优势的分析，在伯尔曼和费尔南德斯，Numer。Math. 107（2007），39-77，用于Navier-Stokes问题的边缘稳定有限元近似。一些数值实验补充了理论结果。© 2014 Wiley Periodicals，Inc. Numer Methods Partial Differential Eq 31：1224-1250，2015
We consider conforming finite element (FE) approximations of the time‐dependent, incompressible Navier–Stokes problem with inf‐sup stable approximation of velocity and pressure. In case of high Reynolds numbers, a local projection stabilization method is considered. In particular, the idea of streamline upwinding is combined with stabilization of the divergence‐free constraint. For the arising nonlinear semidiscrete problem, a stability and convergence analysis is given. Our approach improves some results of a recent paper by Matthies and Tobiska (IMA J. Numer. Anal., to appear) for the linearized model and takes partly advantage of the analysis in Burman and Fernández, Numer. Math. 107 (2007), 39–77 for edge‐stabilized FE approximation of the Navier–Stokes problem. Some numerical experiments complement the theoretical results. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1224–1250, 2015