离散分解性质和混合元的敛速估计

doi:10.12286/jssx.1984.3.300

计算数学 ›› 1984, Vol. 6 ›› Issue (3): 300-305.DOI: 10.12286/jssx.1984.3.300

离散分解性质和混合元的敛速估计

周天孝

中国航空研究院计算研究所

出版日期:1984-03-14 发布日期:1984-03-14

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周天孝. 离散分解性质和混合元的敛速估计[J]. 计算数学, 1984, 6(3): 300-305.

GRID DECOMPOSITION PROPERTY AND ERROR ESTIMATES FOR MIXED FINITE ELEMENT METHODS

Zhou Tian-xiao Computing Institute, Chinese Aeronautical Establishment

Online:1984-03-14 Published:1984-03-14

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:

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.

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离散分解性质和混合元的敛速估计

GRID DECOMPOSITION PROPERTY AND ERROR ESTIMATES FOR MIXED FINITE ELEMENT METHODS

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