单位：University of Iowa，USA

时间：2016年6月9日 上午10；00-11；30； 下午13：30-15：00

地点：下沙校区教学D楼204学术报告厅

摘要：

Inequality problems in mechanics can be divided into two main classes: that of variational inequalities which is concerned with convex energy functionals (potentials), and that of hemivariational inequalities which is concerned with nonsmooth and nonconvex energy functionals (superpotentials).Through the formulation of hemivariational inequalities, problems involving nonmonotone, nonsmooth and multivalued constitutive laws, forces, and boundary conditions can be treated successfully. During the last three decades, hemivariational inequalities were shown to be very useful across a wide variety of subjects, ranging from nonsmooth mechanics, physics, engineering, to economics.

The first part of the talks is devoted to a gentle description of the basic notions and ideas of the theory of hemivariational inequalities. Starting with a simple model of elliptic boundary value problem, we gradually introduce formulations of variational inequalities and hemivariational inequalities, generalized (Clarke) directional derivatives and subdifferentials, existence result for inclusion relation, and hemivariational inequalities in contact mechanics.

The second part of the talks is devoted to numerical analysis of hemivariational inequalities. We present new results on convergence and error estimates for numerical solutions of hemivariational inequalities, with applications in solid mechanics as well as fluid mechanics. Optimal order error estimates are derived for finite element solutions using the linear elements. Numerical examples are shown on the performance of the numerical methods, including numerical convergence orders.