论非线性多重网格法的逼近性质

多重网格法是一种求解椭圆边值问题离散所得的大型线性或非线性方程组的“最优”解法。在有限元离散情形,Hackbusch提出了一种多重网格法的收敛分析方法,即把线性或非线性的多重网格法收敛率的估计问题归结为所谓“光滑性质”与“逼近性质”的研究。在线性情形,若已知有限元解的误差估计,一般容易得到多重网格法的“逼近性质”。但对非线性多重网格法的“逼近性质”在什么条件下成立,尚未见到这方面的工

ON THE APPROXIMATION PROPERTY OF NON-LINEAR MULTIGRID METHOD

A sufficient condition on proving the approximation property of non-linearmultigrid method is proposed for solving one kind of finite element non-linearequations. By it, we can get the convergence rate of non-linear multigrid methodwithout knowing the normal order of convergence of the solution of the finiteelement equation to be solved.