一般双线性有限元展开和外推剖分分析

Analysis of Partition for Expansion and Extrapolation of General Bilinear Finite Elements

考虑变系数问题 ,首先假定剖分Th 为拟一致四边形部分 ,将Th 中任意单元e通过双线性变换映照到一个标准单元E ,然后由E上的误差展开得到e上的误差展开 ,最后分析这些展开式 。

A varying confficient problem is considered.First,supposing a quadrilateral partition T h is quasi-uniform family,we map an arbitrary element e∈T h into a standard element E by bilinear transformation.Second,from the error expansions on E,the error expansions on e are obtained.Finally,the analysis of the expansions showes the essential and sufficient conditions of the error expansion and extrapolation over all elements.