Anisotropic mean curvature flow for two-dimensional surfaces in higher codimension: A numerical scheme
type: Item
instance of: scholarly article
title: Anisotropic mean curvature flow for two-dimensional surfaces in higher codimension: A numerical scheme
zbMATH Open document ID: 1158.65076
DOI: 10.4171/IFB/201
author: Paola Pozzi
published in: Interfaces and Free Boundaries
publication date: 2009-01-30T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_pdf.php
review text: The aim of the paper is to derive numerical schemes for the mean curvature flow for two-dimensional surfaces in higher codimension. Since the chosen numerical method is that of finite elements the author needs the weak formulation too. She proves that the numerical method is stable, and numerical simulation illustrates the efficiency of the method. After an introductory section, the author gives in Section 2 a proper definition of the energy functional. In section 3 a brief review of the concepts which helps the reader to gain a geometric intuition are presented. The next section presents the definition of the of the mean curvature vector \(H_{F}\) and that of anisotropic curvature flow. The weak formulation of the flow is given in Section 5. Section 6 is devoted to the the finite element method (FEM) and two FEM schemes are presented. In Section 8 numerical and graphical examples are considered. Finally, Section 9 contains a generalization of Wulff shapes for higher codimension.
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 53C44
zbMATH DE Number: 5500719
zbMATH Keywords: weak formulation
zbMATH Keywords: mean curvature
zbMATH Keywords: graphical tests
zbMATH Keywords: Wulff shapes
zbMATH Keywords: two-dimensional surfaces
zbMATH Keywords: finite element method
zbMATH Keywords: numerical and graphical examples
MaRDI profile type: Publication
OpenAlex ID: W2082435022
description: scientific article; zbMATH DE number 5500719