Ladyzhenskaya模型的非协调有限元逼近

§1.引言 Navier-Stokes方程是描述粘性不可压缩流体运动的偏微分方程,它是研究这类非线性问题的很好的数学模型。但是,当速度梯度较大时,方程的整体解是否唯一可解,这个问题尚未得到解决。为此,对于不可压缩粘性流体的定常情形,Ladyzhenskaya提出利用下面的模型来代替Navier-Stokes方程。 设Ω是R~n(n=2或3)中的有界区域,边界?ΩLipshitz连续,u是流体速度,p是

ON NONCONFORMING FINITE ELEMENT APPROXIMATIONS OF THE LADYZHENSKAYA MODEL FOR STATIONARY INCOMPRESSIBLE VISCOUS FLOW

In this paper, the nonconforming finite element approximations of the ladyzhenskaya modelfor stationary incompressible viscous flow are discussed. The approximation problems are provedto be well posed. For the usual nonconforming Crouzeix-Raviart element, the optimalorder estimates in H~1 W~(1.q) norms for the velocity and in L~2 norm for the pressure are deri-ved under realistic regularity assumptions.