中文摘要：

这份报纸在三角形的网孔上为泊松方程建立一个新有限体积元素计划。试用函数空间在三角形的分区上作为 Lagrangian 立方的有限元素空格被花，并且测试函数空格在双分区上被定义为 piecewise 常数空格。在关于三角形的网孔的一些弱状况下面，作者证明僵硬矩阵是一致地积极的明确并且是 O 的集中率(h 3 ) 在 H 1 标准。一些数字实验证实理论考虑。

英文摘要：

This paper establishes a new finite volume element scheme for Poisson equation on trian- gular meshes. The trial function space is taken as Lagrangian cubic finite element space on triangular partition, and the test function space is defined as piecewise constant space on dual partition. Under some weak condition about the triangular meshes, the authors prove that the stiffness matrix is uni- formly positive definite and convergence rate to be O（h3） in Hi-norm. Some numerical experiments confirm the theoretical considerations.