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离散分解性质和混合元的敛速估计

周天孝   

  1. 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

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

  1. 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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