Analysis of a pressure-stabilized finite element approximation of the stationary Navier-Stokes equations
Analysis of a pressure-stabilized finite element approximation of the stationary Navier-Stokes equations
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DOI：
10.1007/s002110000174
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发表时间：
2000
影响因子：
2.1
通讯作者：
R. Codina;J. Blasco
中科院分区：
文献类型：
--
作者：
R. Codina;J. Blasco
本文的目的是分析有限元近似的定常Navier-Stokes方程，允许使用等速压力插值。这个想法是引入作为未知的离散问题的投影的压力梯度（乘以适当的算法参数）到空间的连续矢量场。在连续性方程中引入了这两个矢量（压力梯度和投影）之间的差异。所得到的配方是稳定的，最佳收敛，无论是在一个规范相关的问题，并在thirumm的速度和压力。首先对Stokes问题证明了这一点，然后将其推广到非线性情形。所有的分析依赖于一个inf-sup条件，这是弱得多的标准Galerkin近似，尽管事实上，本方法只是一个小的修改。
The purpose of this paper is to analyze a finite element approximation of the stationary Navier-Stokes equations that allows the use of equal velocity-pressure interpolation. The idea is to introduce as unknown of the discrete problem the projection of the pressure gradient (multiplied by suitable algorithmic parameters) onto the space of continuous vector fields. The difference between these two vectors (pressure gradient and projection) is introduced in the continuity equation. The resulting formulation is shown to be stable and optimally convergent, both in a norm associated to the problem and in thenorm for both velocities and pressure. This is proved first for the Stokes problem, and then it is extended to the nonlinear case. All the analysis relies on an inf-sup condition that is much weaker than for the standard Galerkin approximation, in spite of the fact that the present method is only a minor modification of this.