基于Poisson方程弱有限元方法的修正研究

A Modified Weak Galerkin Finite Element Method for Poisson Equation

针对Poisson方程的弱有限元方法进行修正,其核心思想是在弱有限元的基础上,边界函数vb用内部函数v0的平均代替来减少该系统的未知量,进而提高计算速度。文章首先利用弱有限元方法离散函数u,然后对u的弱函数空间进行修正,并且建立了相关的误差方程,最后得到了函数u在H1范数和L2范数下的最优估计,这为Poisson方程的数值求解提供理论上的保证。

A modified weak Galerkin finite element method is researched for Poisson equation.This method,which is based on weak Galerkin finite element method,aims to replace the boundary functions vb with the average of the internal function v0.The result is that whole system has fewer degree of freedom,thus to speed calculation.This paper starts by dispersing the function u.Further,corresponding error equations are established and error estimates are analysed for numerical solution of Poisson problems.In conclusion,we obtain the optimal estimation of the function under the H1 norm and L2 norm,which provides more solid theoretical support for solving the Poisson equation.