Error Analysis of Projection Methods for Non inf-sup Stable Mixed Finite Elements: The Navier-Stokes Equations

被引：6
|
作者：
de Frutos, Javier [1 ]
Garcia-Archilla, Bosco [2 ]
Novo, Julia [3 ]
机构：
[1] Univ Valladolid, Inst Invest Matemat IMUVA, Valladolid, Spain
[2] Univ Seville, Dept Matemat Aplicada 2, Seville, Spain
[3] Univ Autonoma Madrid, Dept Matemat, Madrid, Spain
来源：
JOURNAL OF SCIENTIFIC COMPUTING | 2018年 / 74卷 / 01期
关键词：
Projection methods; Non inf-sup stable elements; Navier-Stokes equations; PSPG stabilization; APPROXIMATION; CONVERGENCE; STABILITY;
D O I：
10.1007/s10915-017-0446-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We obtain error bounds for a modified Chorin-Teman (Euler non-incremental) method for non inf-sup stable mixed finite elements applied to the evolutionary Navier-Stokes equations. The analysis of the classical Euler non-incremental method is obtained as a particular case. We prove that the modified Euler non-incremental scheme has an inherent stabilization that allows the use of non inf-sup stable mixed finite elements without any kind of extra added stabilization. We show that it is also true in the case of the classical Chorin-Temam method. The relation of the methods with the so called pressure stabilized Petrov Galerkin method is established. We do not assume non-local compatibility conditions for the solution.
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页码：426 / 455
页数：30
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