Numerical Analysis of Variational and Hemivariational Inequalities with Applications
讲座名称:
Numerical Analysis of Variational and Hemivariational Inequalities with Applications
讲座时间:
2019-06-11
讲座人:
韩渭敏
形式:
校区:
兴庆校区
实践学分:
讲座内容:
讲座题目:Numerical Analysis of Variational and Hemivariational Inequalities with Applications
讲座时间:2019年6月11日-14日,早上 9:00 - 12:00
讲座地点:西安交通大学 数学楼 2-2 会议室
讲座人:韩渭敏
讲座内容:
Inequality problems in mechanics can be divided into two main categories: that of variational inequalities concerned with convex energy functionals (potentials), and that of hemivariational inequalities 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. Hemivariational inequalities have been shown to be very useful across a wide variety of subjects, ranging from nonsmooth mechanics, physics, engineering, to economics. This series of lectures will cover the following topics:
(1) basic notions and results on functional analysis, function spaces, and weak formulations of boundary value problems; (2) a brief introduction of variational and hemivariational inequalities arising in contact mechanics; (3) a review of well-posedness results of sample variational and hemivariational inequalities; (4) numerical analysis of variational and hemivariational inequalities: description of numerical methods, convergence analysis, error estimation; (5) discussion of future research topics.
近年来,关于变分与半变分不等式数学理论与数值方法的研究取得了重大进展,并在诸多领域得到了广泛应用。受西安交通大学数学与统计学院邀请,美国爱荷华大学韩渭敏教授将以“变分与半变分不等式问题的数值分析与应用”为题,面向青年学者及研究生开设系列学术讲座,介绍此领域的最新学术成果及未来研究方向。本系列讲座将聚焦变分与半变分不等式数学理论与数值方法的最新进展及其在科学与工程中的应用,内容包括:(1)泛函分析的基本结果、函数空间、边值问题的弱形式;(2)接触力学中变分与半变分不等式简介;(3)变分与半变分不等式的适定性分析;(4)变分与半变分不等式问题的数值分析;(5)未来研究课题。
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