% formatted on 970304 by morris
\documentstyle{article}
\setcounter{page}{48}
\textheight 9.5in
\textwidth 5.75in
\voffset -1in
\hoffset -0.55in
%\documentstyle{llncs}
\begin{document}
\title{The Finite Element Methods Based on Two-Scale Analysis}
\author{J.Z.~Cui\\
The Institute of Comp. Math. $\&$ Sci.-Engg. Comp., Academia Sinica, China
\and
T.M.~Shih\\
Dept. of applied Math., The Hong Kong Polytechnic Univ., Hong Kong
\and
Y.L.~Wang\\
Dept. of Math., ZhengZhou Univ., Henan, China
}

\date{}
\maketitle
The analysis problems of composite material and the structure with periodic
configurations are often encountered in high technological engineerings and
the industries of new products. In 2 or 3 dimensional case they can lead to
a kind of boundary value problems of partial differential equations with 
the coefficients having small period and sharp variation.  They are difficult
to be solved by ordinary numerical methods.\\

The Two-Scale Analysis (TSA) is a new method under developing for solving
this kind of problems. Based on the asymptotic solution of two-scale
analysis this paper mainly contributes in developing \ corresponding finite
element algorithm and making numerical experiments.  The contents of this
paper are following: \\

\begin{enumerate}
\item{Briefly to show the main formulas of TSA} \\
\item{The finite element computation of homogenization coefficients} \\
\item{The main results of convergence prof on finite element algorithm
relevant to TSA} \\
\item{The main formulas of the finite element computation for two 
dimensional case} \\
\item{The numerical result} \\ 
\end{enumerate}
\end{document}


