FRACTIONAL-STEP METHODS AND FINITE ELEMENTS WITH SYMMETRIC STABILIZATION FOR THE TRANSIENT OSEEN PROBLEM

被引：15

作者：

Burman, Erik ^{[1
]}

Ern, Alexandre ^{[2
]}

Fernandez, Miguel A. ^{[3
,4
]}

机构：

[1] UCL, Dept Math, Gower St, London WC1E 6BT, England

[2] Univ Paris Est, CERMICS ENPC, F-77455 Marne La Vallee 2, France

[3] Inria, F-75012 Paris, France

[4] UPMC, Sorbonnes Univ, Lab Jacques Louis Lions, F-75005 Paris, France

来源：

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2017年 / 51卷 / 02期

关键词：

Oseen equations; stabilized finite elements; fractional-step methods; pressure-correction methods; error estimates; high Reynolds number; DISCONTINUOUS GALERKIN METHODS; NAVIER-STOKES EQUATIONS; APPROXIMATIONS; CONVECTION; FLOWS;

D O I：

10.1051/m2an/2016028

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with the spatial and time discretization of the transient Oseen equations. Finite elements with symmetric stabilization in space are combined with several time-stepping schemes (monolithic and fractional-step). Quasi-optimal (in space) and optimal (in time) error estimates are established for smooth solutions in all flow regimes. We first analyze monolithic time discretizations using the Backward Differentation Formulas of order 1 and 2 (BDF1 and BDF2). We derive a new estimate on the time-average of the pressure error featuring the same robustness with respect to the Reynolds number as the velocity estimate. Then, we analyze fractional-step pressure-projection methods using BDF1. The stabilization of velocities and pressures can be treated either implicitly or explicitly. Numerical results illustrate the main theoretical findings.

引用

页码：487 / 507

页数：21

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