About: Numerical Simulation of Anisotropic Mean Curvature of Graphs in Relative Geometry

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://www.uni-obuda.hu/journal/Issue45.htm
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 Finsler Geometry, 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., Dziuk, G.: Discrete Anisotropic Curvature Ow of Graphs, ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 33, No. 6, pp. 1203-1222, 1999 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 Finsler Geometry, 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., Dziuk, G.: Discrete Anisotropic Curvature Ow of Graphs, ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 33, No. 6, pp. 1203-1222, 1999 (en)
Title	Numerical Simulation of Anisotropic Mean Curvature of Graphs in Relative Geometry Numerical Simulation of Anisotropic Mean Curvature of Graphs in Relative Geometry (en)
skos:prefLabel	Numerical Simulation of Anisotropic Mean Curvature of Graphs in Relative Geometry Numerical Simulation of Anisotropic Mean Curvature of Graphs in Relative Geometry (en)
skos:notation	RIV/68407700:21340/13:00206464!RIV14-GA0-21340___
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(GAP108/12/1463)
http://linked.open...iv/cisloPeriodika	7
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Oberhuber, Tomáš Beneš, Michal Hoang, Dieu Hung
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	České vysoké učení technické v Praze / Fakulta jaderná a fyzikálně inženýrská
http://linked.open...dnocenehoVysledku	92574
http://linked.open...ai/riv/idVysledku	RIV/68407700:21340/13:00206464
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	anisotropy; mean curvature; Finsler geometry; method of lines; FDM (en)
http://linked.open.../riv/klicoveSlovo	mean curvature anisotropy method of lines FDM Finsler geometry
http://linked.open...odStatuVydavatele	HU - Maďarsko
http://linked.open...ontrolniKodProRIV	[02F585E356DA]
http://linked.open...i/riv/nazevZdroje	Acta Polytechnica Hungarrica
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	3 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Two scales discrete-continuum approach to dislocation dynamics
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	10
http://linked.open...iv/tvurceVysledku	Beneš, Michal Oberhuber, Tomáš Hoang, Dieu Hung
http://linked.open...ain/vavai/riv/wos	000329890400008
issn	1785-8860
number of pages	17 (xsd:int)
http://bibframe.org/vocab/doi	10.12700/APH.10.07.2013.7.8
http://localhost/t...ganizacniJednotka	21340

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