有限元分层快速高精度算法

THE HIERARCHICAL FAST FINITE ELEMENT METHOD WITH HIGH ACCURACY

1.引言 多重网格法和区域分解法实质是有限元空间的分解,在子空间上实行逐次校正迭代或并行校正迭代。[1]对一维有限元空间,利用正交化过程,消去单元内结点,修改单元角点的基函数,提出了所谓快速高精度算法。实例表明,这一算法十分有效。本文对一般区域Ω R^d(d=1,2,3)上有限元空间进行分层正交分解,提出所谓分层快速高精度算法。

Using the orthogonal splitting theory of the finite element space; we provide the hier- archical fast finite element method with high accuracy in R^d(d=1, 2, 3). We need only to solve the linear subsystems hierarchically instead of solving the algebraic system of equa- tions, which arise from the discretization of symmetric elliptic boundary value problems via finite.element methods. A numerical example is presented to illustrate the theoretically predicted results.