Hemivariational Inequalities: Theory and Numerical Analysis
讲座名称：
Hemivariational Inequalities: Theory and Numerical Analysis
讲座时间：
2016-07-07
讲座人：
韩渭敏
形式：
校区：
兴庆校区
实践学分：
讲座内容：
为促进学术交流，带动我院在相关领域的科学研究，数学与统计学院长江学者讲座教授韩渭敏博士将面向全院做如下学术讲座。
报告题目：Hemivariational Inequalities: Theory and Numerical Analysis
报告时间：2016年7月7日，16:30—18:00
报告地点：理科楼407
报告内容：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 talk includes an introduction of the basic notions, ideas and results of the theory of hemivariational inequalities, and focuses on 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.
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