离散分解性质和混合元的敛速估计

一、引言 4]称:对于混合元,现存文献的误差估计常常低于计算中实际观察到的收敛速率。就Poisson方程基于Kelvin变分原理的混合法而言,有关的理论分析(特别是1—3,5])都利用Babuska-Brezzi条件。但是,对于线性元,这一类条件只导致下列形式的误差估计:

GRID DECOMPOSITION PROPERTY AND ERROR ESTIMATES FOR MIXED FINITE ELEMENT METHODS

In the paper, the role of GDP (Grid Decomposition Property, introduced in 4])played in the convergence analysis of mixed methods is discussed in connection withthe unified theory developed in 6]. It is pointed out that not GDP, but the gene-ralized Allmann-Johnson condition, plays a crucial role in achieving the optimal errorbounds, nevertheless GDP is important and sufficient for the Babuska-Brezzi condi-tion. The optimal error estimates in 4] are achieved by using two mesh-dependentnorms.