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Model. Anal. Inform. Sist., 2017, Volume 24, Number 3, Pages 322–338 (Mi mais567)  

Dynamically adapted mesh construction for the efficient numerical solution of a singular perturbed reaction-diffusion-advection equation

D. V. Luk'yanenko, V. T. Volkov, N. N. Nefedov

Lomonosov Moscow State University, Faculty of Physics, 1, bld. 2 Leninskiye Gory, Moscow, GSP-1, 119991, Russia

Abstract: This work develops a theory of the asymptotic-numerical investigation of the moving fronts in reaction-diffusion-advection models. By considering the numerical solution of the singularly perturbed Burgers's equation we discuss a method of dynamically adapted mesh construction that is able to significantly improve the numerical solution of this type of equations. For the construction we use a priori information that is based on the asymptotic analysis of the problem. In particular, we take into account the information about the speed of the transition layer, its width and structure. Our algorithms are able to reduce significantly complexity and enhance stability of the numerical calculations in comparison with classical approaches for solving this class of problems. The numerical experiment is presented to demonstrate the effectiveness of the proposed method.
The article is published in the authors' wording.

Keywords: singularly perturbed, interior layer, dynamically adapted mesh.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00755_а
16-01-00437_а
17-51-53002_ГФЕН_а
17-01-00159_а
This work was supported by RFBR, projects No. 16-01-00755, 16-01-00437, 17-51-53002 and 17-01-00159.


DOI: https://doi.org/10.18255/1818-1015-2017-3-322-338

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UDC: 519.6
Received: 15.12.2016
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Citation: D. V. Luk'yanenko, V. T. Volkov, N. N. Nefedov, “Dynamically adapted mesh construction for the efficient numerical solution of a singular perturbed reaction-diffusion-advection equation”, Model. Anal. Inform. Sist., 24:3 (2017), 322–338

Citation in format AMSBIB
\Bibitem{LukVolNef17}
\by D.~V.~Luk'yanenko, V.~T.~Volkov, N.~N.~Nefedov
\paper Dynamically adapted mesh construction for the efficient numerical solution of a singular perturbed reaction-diffusion-advection equation
\jour Model. Anal. Inform. Sist.
\yr 2017
\vol 24
\issue 3
\pages 322--338
\mathnet{http://mi.mathnet.ru/mais567}
\crossref{https://doi.org/10.18255/1818-1015-2017-3-322-338}
\elib{http://elibrary.ru/item.asp?id=29332975}


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