Error estimate of the finite volume scheme for the Allen–Cahn equation

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F18%3A00319370" target="_blank" >RIV/68407700:21340/18:00319370 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s10543-017-0687-4" target="_blank" >https://doi.org/10.1007/s10543-017-0687-4</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10543-017-0687-4" target="_blank" >10.1007/s10543-017-0687-4</a>

Result language
angličtina
Original language name
Error estimate of the finite volume scheme for the Allen–Cahn equation
Original language description
The Allen-Cahn equation originates in the phase field formulation of phase transition phenomena. It is a reaction-diffusion PDE with a nonlinear reaction term which allows the formation of a diffuse phase interface. We first introduce a model initial boundary-value problem for the isotropic variant of the equation. Its numerical solution by the method of lines is then considered, using a finite volume scheme for spatial discretization. An error estimate is derived for the solution of the resulting semidiscrete scheme. Subsequently, sample numerical simulations in two and three dimensions are presented and the experimental convergence measurement is discussed.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GB14-36566G" target="_blank" >GB14-36566G: Multidisciplinary research centre for advanced materials</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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