三维矩形域上泊松方程四面体线元的超逼近与外推

Superclose and Extrapolation of the Tetrahedral Linear Finite Elements for Poisson Equation in Three-dimensional Rectangular Field

改进三角元的积分恒等式,使之适用于拟一致四面体元,借此证明了泊松方程四面体线元梯度有超逼近现象,函数值Richardson外推可以提高精度.

In this paper, the integral identities of triangular linear elements are improved, so they also apply to quasi-uniform tetrahedral linear elements. Then the authors show that the tetrahedral linear finite element solution uh and the tetrahedral linear interpolation u1 have superclose gradient for Poisson Equation and obtain the improved accuracy through Richardson extrapolation of the tetrahedral linear finite element solution uh.