有限体积法及其在边值问题中的应用本文介绍了极小位能原理、虚功原理和Ritz-Galerkin方法．主要讨论了椭圆型方程定解问题的有限体积法和双曲型方程定解问题的有限体积法，简要说明了椭圆型方程定解问题的有限体积法的收敛性和近似解误差估计．另外，针对矩形域上一个泊松方程的具体定解问题，导出了它的一种特殊有限体积格式，并且编程实现，计算出该泊松方程定解问题的数值解，将算出的数值解与问题的精确解进行了简单比较，得到了初步的结论．在具体例子中用的是一种特殊的有限体积格式，它可以化为五点差分格式，它比较简单，但有很大的局限性，在边界很规则的情况下使用效果比较好，当边界不规则时，五点差分格式的误差就比较大．一般情况的有限体积法在本文没有太多涉及．-Finite volume method

and its application in the problem for determining solution

The thesis introduced principal of minimum potential energy , principle of virtual work and Ritz-Galerkin method. It is mainly discussed finite volume method of problem for determining solution of elliptic equation and of hyperbolic equation. It is briefly stated that the convergence and error of numerical solutions for elliptic equation. Besides that, it is derived that a special scheme of finite volumn for solving the poisson equation in the rectangle domain, and is obtained the numerical solution by programming. After that, I compared the excise solution with the numerical solution, and came to a simple conclusion. This five point scheme is deduced in the thesis, though it’s simple, it has its limit. It works well when the boundary is regular and its error become large when the boundary is irregular. The thesis hasn’t dealt with finite volumn method in general condition.