Numerical Simulation of Anisotropic Mean Curvature of Graphs in Relative Geometry

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F13%3A00206464" target="_blank" >RIV/68407700:21340/13:00206464 - isvavai.cz</a>

Výsledek na webu

<a href="http://www.uni-obuda.hu/journal/Issue45.htm" target="_blank" >http://www.uni-obuda.hu/journal/Issue45.htm</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.12700/APH.10.07.2013.7.8" target="_blank" >10.12700/APH.10.07.2013.7.8</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Numerical Simulation of Anisotropic Mean Curvature of Graphs in Relative Geometry

Popis výsledku v původním jazyce

The aim of this paper is the numerical simulation of anisotropic mean curvature of graphs in the context of relative geometry, developed in [1]. We extend results in [3] to our problem; we prove an existence theorem and energy equality. The numerical scheme is based on the method of lines where the spatial derivatives are approximated by finite differences [2]. We then solve the resulting ODE system by means of the adaptive Runge-Kutta-Merson method. To show the stability of the scheme we prove the discrete version of the energy equality. Finally, we show experimental order of convergence and results of numerical experiments with various anisotropy settings. [1] Bellettini, G., Paolini, M.: Anisotropic Motion by Mean Curvature in the Context of FinslerGeometry, Hokkaido Mathematical Journal, Vol. 25, No. 3, pp. 537-566, 1996 [2] Beneš, M.: Diffuse-Interface Treatment of the Anisotropic Mean-Curvature Flow, Applications of Mathematics, Vol. 48, pp. 437-453, 2003 [3] Deckelnick, K., Dzi

Název v anglickém jazyce

Numerical Simulation of Anisotropic Mean Curvature of Graphs in Relative Geometry

Popis výsledku anglicky

The aim of this paper is the numerical simulation of anisotropic mean curvature of graphs in the context of relative geometry, developed in [1]. We extend results in [3] to our problem; we prove an existence theorem and energy equality. The numerical scheme is based on the method of lines where the spatial derivatives are approximated by finite differences [2]. We then solve the resulting ODE system by means of the adaptive Runge-Kutta-Merson method. To show the stability of the scheme we prove the discrete version of the energy equality. Finally, we show experimental order of convergence and results of numerical experiments with various anisotropy settings. [1] Bellettini, G., Paolini, M.: Anisotropic Motion by Mean Curvature in the Context of FinslerGeometry, Hokkaido Mathematical Journal, Vol. 25, No. 3, pp. 537-566, 1996 [2] Beneš, M.: Diffuse-Interface Treatment of the Anisotropic Mean-Curvature Flow, Applications of Mathematics, Vol. 48, pp. 437-453, 2003 [3] Deckelnick, K., Dzi

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GAP108%2F12%2F1463" target="_blank" >GAP108/12/1463: Dvouúrovňová diskrétně-spojitá dislokační dynamika</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2013

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Acta Polytechnica Hungarrica

ISSN

1785-8860

e-ISSN

—

Svazek periodika

10

Číslo periodika v rámci svazku

7

Stát vydavatele periodika

HU - Maďarsko

Počet stran výsledku

17

Strana od-do

99-115

Kód UT WoS článku

000329890400008

EID výsledku v databázi Scopus

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