THE COMBINED METHOD BETWEEN ORIGINAL ENERGY METHOD AND FINITE ELEMENT METHOD FOR SOLVING LAPLACE''S BOUNDARY VALUES WITH SINGULARITIES
具有奇点的Laplace方程边值问题的原始能量-有限元结合法

Recently great attention has been paid to the Studies on numerical methodsfor solving the equations with singularities. We shall use the Combined Method betweenOriginal Energy Method (i. e., Ritz-Galerkin Method) and Finite Element Method. Theestimated errors and stability of their numerical solution are given in this paper. The averageerrors of approximate solutions and their generalized derivatives by the Combined Method wouldbe O(h) if L+ 1 = 0(|lnh|), where L+1 is the total of singular basis functions used inOriginal Energy Method, h the upper bound of boundary lengths in the triangulation of FiniteElement Method. This method is much simpler than Infinite Similar Division Method. It isshown in the concrete calculation of Motz Problem that the numerical solution calculated bythis combined method has better precision.