一维有限元分层快速高精度算法

THE HIERARCHICAL FAST FINITE ELEMENT METHOD WITH HIGH ACCURACY IN ONE DIMENSION

本文利用一维有限元空间的正交分解理论,提出并分析了所谓分层快速高精度算法.采用这一方法,无需求解有限元离散方程,只需分层地解子系统,结点上超收敛估计可分层得到,数例表明该方法的有效性。

Using orthogonal splitting theory of finite element space,weprovide the hierarchical fast finite element method with high accuracy inone dimension.Only we need to solve the subsystems hierarchically, nee-dless to solve the algebraic system of equations,which arise from the dis-cretization of two-point boundary value problems via finite element met-hods.Numerical example is presented which illustrate the theoreticallypredicted the results.