A First-order Two-scale Analysis for Contact Problems with Small Periodic Structure
Changqing Ye, Junzhi Cui · arXiv (Cornell University) · 2019
This paper is devoted to study a type of contact problem modeling by hemivariational inequalities with small periodic coefficients appearing in the controlling PDE, and the PDE we considered is linear, second order and uniformal elliptic. Under the assumptions, it is proved that previous problem can be homogenized, and the solutions weakly converge. We derive an $O(\epsilon^{1/2})$ estimation to facilitate building the computational framework. It is shown that Robin problem--- a special case of contact problems, leads to the same $O(\epsilon^{1/2})$ estimation. Our computational framework relies on finite element methods, and the numerical analysis is given.