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Hessian recovery based finite element methods for the Cahn-Hilliard equation
发布时间:2019-06-11 13:49:39 364

演讲人Speaker:   郭海龙

题目Title: Hessian recovery based finite element methods for the Cahn-Hilliard equation

时间Date: 2019  年 6 月 18  日       Time:16:00-17:00

地点Venue:  A 栋 307  室

内容摘要Abstract:

In this talk, we talk about some new recovery based finite element methods for the 2D Cahn-Hilliard equation. One distinguishing feature of those methods is that we discretize the fourth-order differential operator in a standard C0 linear finite elements space. Precisely, we first transform the fourth-order Cahn-Hilliard equation to its variational formulation in which only first-order and second-order derivatives are involved and then we compute the first and second-order derivatives of a linear finite element function by a least-squares fitting recovery procedure. When the underlying mesh is uniform meshes of regular pattern, our recovery scheme for the Laplacian operator coincides with the well- known five-point stencil. Another feature of the methods is some special treatments on Neumann type boundary conditions for reducing computational cost. The optimal-order convergence and energy stability are numerically proved through a series of benchmark tests. The proposed method can be regarded as a combination of the finite difference scheme and the finite element scheme. Extension to surface setting is also addressed.

 

个人简介(About the speaker):

郭海龙博士,墨尔本大学讲师,2007年和2010年分别本科和硕士毕业于湖南师范大学、北京大学,2014年5月和2015年8月分别获得韦恩州立大学统计数学硕士和数学博士学位,2015年7月-2018年6月在加州大学圣芭芭拉分校从事博士后研究,之后一直在墨尔本大学工作至今。郭海龙博士主要从事偏微分方程数值解,后验自适应方法的设计和分析,拓扑材料中的波动问题、高频波动问题等等。迄今在国际知名杂志包括MC、M3AS、JCP等,发表SCI论文近20篇,主持一项Andrew Sisson国家基金。