摘要
本文主要讨论层状复合材料稳态热传导问题的实际计算.首先利用均匀化和多尺度渐近展开法求解层状复合材料非齐次边界的Dirichlet问题,得到其均匀化方程和渐近展开式,并给出了一个详尽的收敛性分析.其次利用混合有限元方法对齐次边界Diricblet问题的均匀化方程进行分析,给出了一种求解格式,这种单元具有各向异性特征,解除了正则性条件的束缚,用各向异性插值定理给出了误差分析.
The main part of this paper deals with computation of the heat transfer problems of the layered composite materials. Firstly,we discuss non-homogeneous boundary Dirichlet problem of layered composite materials by using of asymptotic expansion and homogenization and obtain the homogenized equation and the asymptotic expansion. We provide a detailed convergence analysis of this problem. Secondly,a kind of homogenized equation of homogenous boundary Dirichlet problem can be analysed by mixed finite element method. We give an numerical scheme. This element spaces have the characteristic of anisotropic, that is to say,the domain subdivision need not satisfy the regular condition. The anisotropic interpolation theory can be used to give error estimation.
引文
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