小周期接触问题的一阶双尺度分析
A First-order Two-scale Analysis for Contact Problems with Small Periodic Configurations
摘要：
研究了一类具有小周期系数的半变分不等式接触问题，所考虑的偏微分方程是线性的、二阶的、一致椭圆的.在此假设下，证明了原问题是齐次的，且解是弱收敛的。我们推导出一个$O(ε^{1/2})$估计，这是关键的计算框架的建设。我们还证明了Robin问题--接触问题的一种特殊情况，它在$L^2$范数下得到了一个$O(ε)$估计.我们的计算框架是基于有限元法，并给出了数值分析，连同实验来说服估计。
英文摘要：
This paper is devoted to studying a type of contact problems modeled by hemivariational inequalities with small periodic coefficients appearing in PDEs, and the PDEs we considered are linear, second order and uniformly elliptic. Under the assumptions, it is proved that the original problem can be homogenized, and the solution weakly converges. We derive an $O(ε^{1/2})$ estimation which is pivotal in building the computational framework. We also show that Robin problems--- a special case of contact problems, it leads to an $O(ε)$ estimation in $L^2$ norm. Our computational framework is based on finite element methods, and the numerical analysis is given, together with experiments to convince the estimation.
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