High-Order Fully Discrete Energy Diminishing Evolving Surface Finite Element Methods for a Class of Geometric Curvature Flows
Year: 2021
Author: Beiping Duan, Buyang Li, Zhimin Zhang
Annals of Applied Mathematics, Vol. 37 (2021), Iss. 4 : pp. 405–436
Abstract
This article concerns the construction of high-order energy-decaying numerical methods for gradient flows of evolving surfaces with curvature-dependent energy functionals. The semidiscrete evolving surface finite element method is derived based on the calculus of variation of the semidiscrete surface energy functional. This makes the semidiscrete problem naturally inherit the energy decay structure. With this property, the semidiscrete problem is furthermore formulated as a gradient flow system of ODEs. The 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 time. Extensive 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aam.OA-2021-0007
Annals of Applied Mathematics, Vol. 37 (2021), Iss. 4 : pp. 405–436
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 32
Keywords: Gradient flow evolving surface curvature energy decay finite element method averaged vector-field collocation.
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