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Error analysis of non inf-sup stable discretizations of the time-dependent Navier–Stokes equations with local projection stabilization
IMA Journal of Numerical Analysis ( IF 2.1 ) Pub Date : 2018-07-19 , DOI: 10.1093/imanum/dry044
Javier de Frutos 1 , Bosco García-Archilla 2 , Volker John 3, 4 , Julia Novo 5
Affiliation  

This paper studies non inf-sup stable finite element approximations to the evolutionary Navier–Stokes equations. Several local projection stabilization (LPS) methods corresponding to different stabilization terms are analyzed, thereby separately studying the effects of the different stabilization terms. Error estimates are derived in which the constants are independent of inverse powers of the viscosity. For one of the methods, using velocity and pressure finite elements of degree |$l$|⁠, it will be proved that the velocity error in |$L^\infty (0,T;L^2(\varOmega ))$| decays with rate |$l+1/2$| in the case that |$\nu \le h$|⁠, with |$\nu$| being the dimensionless viscosity and |$h$| being the mesh width. In the analysis of another method it was observed that the convective term can be bounded in an optimal way with the LPS stabilization of the pressure gradient. Numerical studies confirm the analytical results.

中文翻译:

具有局部投影稳定的时变Navier–Stokes方程的非infsup稳定离散的误差分析

本文研究了演化Navier–Stokes方程的非insup稳定有限元逼近。分析了对应于不同稳定项的几种局部投影稳定(LPS)方法,从而分别研究了不同稳定项的影响。得出误差估计,其中常数与粘度的反幂无关。对于其中一种方法,使用度数为| $ l $ |⁠的速度和压力有限元,将证明| $ L ^ \ infty(0,T; L ^ 2(\ varOmega))$中的速度误差| 随速率| $ l + 1/2 $ |衰减 如果| $ \ nu \ le h $ |⁠|| $ \ nu $ | 是无因次粘度和| $ h $ |是网格宽度。在对另一种方法的分析中,观察到对流项可以通过压力梯度的LPS稳定化以最佳方式限制。数值研究证实了分析结果。
更新日期:2020-04-17
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