半解析法及其误差估计

解析法是求解偏微分方程最古老的方法,在电子计算机出现以前,它是解微分方程最主要的方法.所有微分方程的经典教科书都讲述这一方法.电子计算机的出现,引起了数值计算方法的发展,解偏微分方程的直接数值方法——差分法和有限元法,渐渐取代了

SEMI ANALYSIS METHOD AND ITS ERROR ESTIMATION

In this paper we propose a method which associates the classical analysismethod with the recent finite element method (i. e. in regular domains and irregular onesanalysis method and finite element are used respectively.) for solving elliptic equations. We alsogive the error estimation in this method and establish the following important result: the semianalysis has much less degrees of freedom than the finite elements under the same requirementfor aceuracy.