High-Order Fully Discrete Energy Diminishing Evolving Surface Finite Element Methods for a Class of Geometric Curvature Flows

作     者：Beiping Duan Buyang Li Zhimin Zhang 

作者机构：Beijing Computational Science Research CenterBeijing 100193China Shenzhen JL Computational Science and Applied Research InstituteShenzhenGuangdong 518129China Department of Applied MathematicsThe Hong Kong Polytechnic UniversityHung HornHong KongChina Department of MathematicsWayne State UniversityDetroitMI 48202USA 

出 版 物：《Annals of Applied Mathematics》 (应用数学年刊（英文版）)

年 卷 期：2021年第37卷第4期

页      面：405-436页

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：partly supported by NSFC 11871092 and NSAF U1930402,China Postdoctoral Science Foundation(Project No.2020M682895) a grant from the Research Grants Council of the Hong Kong Special Administrative Region,China(GRF Project No.Poly U15300920) 

主　　题：Gradient flow evolving surface curvature energy decay evolving surface finite element method averaged vector-field collocation 

摘      要：This article concerns the construction of high-order energy-decaying numerical methods for gradient flows of evolving surfaces with curvature-dependent energy *** semidiscrete evolving surface finite element method is derived based on the calculus of variation of the semidiscrete surface energy *** makes the semidiscrete problem naturally inherit the energy decay *** this property,the semidiscrete problem is furthermore formulated as a gradient flow system of *** averaged vector-field collocation method is used for time discretization of the ODEs to preserve energy decay at the fully discrete level while achieving high-order accuracy in *** numerical examples are provided to illustrate the accuracy and energy diminishing property of the proposed method,as well as the effectiveness of the method in capturing singularities in the evolution of closed surfaces.