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众所周知,流体润滑问题的基本机理是研究形成流体薄膜问题,而雷诺方程(O.Reynolds)是描述流体润滑基本规律的椭圆型偏微分方程。近年来,用有限元素法求解雷诺方程是能得到很佳逼近的数直解,是很有成效的数值解法。而有限元素法是一种基于变分方法的逼近,自然有限元解和它的逼近误差估计均在某种Sobolev范H~l(Ω)0≤l≤m意义下给。但是流体动力润滑问题往往要求有限元解在求解区域Ω的某些点上的精确度或者在这些出点上梯度的精确度。亦即能否给出雷诺方程有限元解的点态误差估计?本文肯定地回答这一问题。
It is well-known that the basic mechanism of the problem of fluid lubrication is to study the problem of forming a fluid film. O. Reynolds equation is an elliptic partial differential equation that describes the basic law of fluid lubrication. In recent years, Finite element method for solving the Reynolds equation can get a good approximation of the number of direct solutions, is a very effective numerical solution. The finite element method is based on the variational approach approximation. Both the natural finite element solution and its approximation error estimation are given in the sense of a Sobolev van H ~ l (Ω) 0≤l≤m. But hydrodynamic lubrication problems often require the accuracy of the finite element solution at some point in the solution region Ω or the gradient at these points. That is, we can give a point state error estimate of the finite element solution of the Reynolds equation? This paper affirms this question positively.