{"title":"On the numerical approximation of hyperbolic mean curvature flows for surfaces","authors":"Klaus Deckelnick , Robert Nürnberg","doi":"10.1016/j.cma.2025.117800","DOIUrl":null,"url":null,"abstract":"<div><div>The paper addresses the numerical approximation of two variants of hyperbolic mean curvature flow of surfaces in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. For each evolution law we propose both a finite element method, as well as a finite difference scheme in the case of axially symmetric surfaces. We present a number of numerical simulations, including convergence tests as well as simulations suggesting the onset of singularities.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"437 ","pages":"Article 117800"},"PeriodicalIF":7.3000,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer Methods in Applied Mechanics and Engineering","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0045782525000726","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/2/8 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
The paper addresses the numerical approximation of two variants of hyperbolic mean curvature flow of surfaces in . For each evolution law we propose both a finite element method, as well as a finite difference scheme in the case of axially symmetric surfaces. We present a number of numerical simulations, including convergence tests as well as simulations suggesting the onset of singularities.
期刊介绍：
Computer Methods in Applied Mechanics and Engineering stands as a cornerstone in the realm of computational science and engineering. With a history spanning over five decades, the journal has been a key platform for disseminating papers on advanced mathematical modeling and numerical solutions. Interdisciplinary in nature, these contributions encompass mechanics, mathematics, computer science, and various scientific disciplines. The journal welcomes a broad range of computational methods addressing the simulation, analysis, and design of complex physical problems, making it a vital resource for researchers in the field.
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