二阶椭圆型偏微分方程有限分析解法的稳定性研究

该文对二阶椭圆型偏微分方程在有限分析单元上，求离散分析解的方格进行了研究。有限分析方法的突出特点是在有限单元边界上构造满足节点函数值的近似边界函数，用分离变量的方法，求得满足近似边界函数条件的中心节点处的分析解。从理论上证明了节点函数值的微小变化以及边界函数值的选取对中心节点处解的影响是稳定的。

Stability Study of FA Method for Second Order Elliptic Partical Differential Equations

This paper studies the analytical solution method in discrete elements with finite analytic (FA) method for second order elliptic partial differential equations. The remarkable feature of FA method is to derive an analytic solution for the center node point of the cell with an approximate boundary function which satisfies the boundary node value of the cell. This paper proves theoretically that the FA solution in the center point of the FA element is stable to the functional value of the boundary node point and to the change of the boundary function.