Numerical Simulation of Anisotropic Mean Curvature of Graphs in Relative Geometry
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Numerical Simulation of Anisotropic Mean Curvature of Graphs in Relative Geometry
Original language description
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
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GAP108%2F12%2F1463" target="_blank" >GAP108/12/1463: Two scales discrete-continuum approach to dislocation dynamics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Acta Polytechnica Hungarrica
ISSN
1785-8860
e-ISSN
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Volume of the periodical
10
Issue of the periodical within the volume
7
Country of publishing house
HU - HUNGARY
Number of pages
17
Pages from-to
99-115
UT code for WoS article
000329890400008
EID of the result in the Scopus database
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