中文摘要：

本文提出了求解Poisson方程的一种新的双二次元有限体积法.新方法与通常的双二次元有限体积法作对偶剖分的方式不同,其主要特点是取应力佳点（Gauss点）作为对偶单元的节点,试探函数空间取双二次有限元空间,检验函数空间取相应于对偶剖分的分片常数函数空间.证明了新方法具有最优的H^1模和L^2模误差估计,讨论了在应力佳点数值梯度的超收敛性估计,并通过数值实验验证了理论分析的结果.

英文摘要：

In this paper,a new kind of biquadratic finite volume element method based on optimal stress points is presented for solving poisson equations,choosing trial and test spaces as the biquadratic finite element space and the piecewise constant function space respectively. It is proved that the method has optimal H^1 and L^2 error estimates.It is also showed the superconvergence of numerical gradients at optimal stress points.Finally,the numerical experiments show the results of theoretical analysis.