Numerical solution for the anisotropic Willmore flow of graphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F15%3A00222650" target="_blank" >RIV/68407700:21340/15:00222650 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.apnum.2014.10.001" target="_blank" >http://dx.doi.org/10.1016/j.apnum.2014.10.001</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.apnum.2014.10.001" target="_blank" >10.1016/j.apnum.2014.10.001</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Numerical solution for the anisotropic Willmore flow of graphs

Popis výsledku v původním jazyce

The Willmore flow is well known problem from the differential geometry. It minimizes the Willmore functional defined as integral of the mean-curvature square over given manifold. For the graph formulation, we derive modification of the Willmore flow withanisotropic mean curvature. We define the weak solution and we prove an energy equality. We approximate the solution numerically by the complementary finite volume method. To show the stability, we re-formulate the resulting scheme in terms of the finite difference method. By using simple framework of the finite difference method (FDM) we show discrete version of the energy equality. The time discretization is done by the method of lines and the resulting system of ODEs is solved by the Runge?Kutta?Merson solver with adaptive integration step. We also show experimental order of convergence as well as results of the numerical experiments, both for several different anisotropies.

Název v anglickém jazyce

Numerical solution for the anisotropic Willmore flow of graphs

Popis výsledku anglicky

The Willmore flow is well known problem from the differential geometry. It minimizes the Willmore functional defined as integral of the mean-curvature square over given manifold. For the graph formulation, we derive modification of the Willmore flow withanisotropic mean curvature. We define the weak solution and we prove an energy equality. We approximate the solution numerically by the complementary finite volume method. To show the stability, we re-formulate the resulting scheme in terms of the finite difference method. By using simple framework of the finite difference method (FDM) we show discrete version of the energy equality. The time discretization is done by the method of lines and the resulting system of ODEs is solved by the Runge?Kutta?Merson solver with adaptive integration step. We also show experimental order of convergence as well as results of the numerical experiments, both for several different anisotropies.

Druh

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

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název periodika

Applied Numerical Mathematics

ISSN

0168-9274

e-ISSN

—

Svazek periodika

88

Číslo periodika v rámci svazku

February

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

17

Strana od-do

1-17

Kód UT WoS článku

000346550500001

EID výsledku v databázi Scopus

2-s2.0-84908544245