有限体积法实现变系数椭圆型方程数值解

A Finite Volume Method of Numerical Solution for Solving Variable Coefficient Elliptic Equations

研究了变系数椭圆型偏微分方程的有限体积法,该方法将研究区域划分为一系列不重复的分割区域,并且每个网格点都包含在一个分割区域,再用待求的偏微分方程对每个分割区域进行积分,便可得到一组离散方程。基于这些离散方程,采用matlab编程达到数值实现的目的。最后,通过数值实例展示了有限体积法的计算精度,并得出了一些普遍且有益的结论。

In this paper,we study the finite volume method for variable coefficient elliptic partial differential equations.Firstly,the study area is divided into a series of sub-regions,which are not overlap for each other,and each grid point is contained in a sub-region.Secondly,we integrate with the unknown partial differential equations for each sub-region,and can get a set of discrete equations.Based on these discrete equations,we achieve numerical implementation with the matlab programming.Finally,a numerical example shows the calculation precision of the finite volume method,and some common and useful conclusions are drawn.