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Model. Anal. Inform. Sist., 2016, Volume 23, Number 3, Pages 334–341 (Mi mais503)  

This article is cited in 5 scientific papers (total in 5 papers)

Analytic-numerical approach to solving singularly perturbed parabolic equations with the use of dynamic adapted meshes

D. V. Lukyanenkoa, V. T. Volkova, N. N. Nefedova, L. Reckeb, K. Schneiderc

a Lomonosov Moscow State University, 119991, Moscow, Leninskie Gory, MSU, Faculty of Physics,
b HU Berlin, Institut für Mathematik, Rudower Chaussee, Berlin, Germany
c Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany

Abstract: The main objective of the paper is to present a new analytic-numerical approach to singularly perturbed reaction-diffusion-advection models with solutions containing moving interior layers (fronts). We describe some methods to generate the dynamic adapted meshes for an efficient numerical solution of such problems. It is based on a priori information about the moving front properties provided by the asymptotic analysis. In particular, for the mesh construction we take into account a priori asymptotic evaluation of the location and speed of the moving front, its width and structure. Our algorithms significantly reduce the CPU time and enhance the stability of the numerical process compared with classical approaches.
The article is published in the authors' wording.

Keywords: singularly perturbed parabolic periodic problems, interior layer, Shishkin mesh, dynamic adapted mesh.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00755_а
14-01-00182_а
16-01-00437_а
14-01-91333_ННИО_а
This work was supported by RFBR, projects No. 16-01-00755, 14-01-00182, RFBR, project No. 16-01-00437, RFBR - DFG, project No. 14-01-91333.


DOI: https://doi.org/10.18255/1818-1015-2016-3-334-341

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UDC: 519.956
Received: 20.05.2016
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Citation: D. V. Lukyanenko, V. T. Volkov, N. N. Nefedov, L. Recke, K. Schneider, “Analytic-numerical approach to solving singularly perturbed parabolic equations with the use of dynamic adapted meshes”, Model. Anal. Inform. Sist., 23:3 (2016), 334–341

Citation in format AMSBIB
\Bibitem{LukVolNef16}
\by D.~V.~Lukyanenko, V.~T.~Volkov, N.~N.~Nefedov, L.~Recke, K.~Schneider
\paper Analytic-numerical approach to solving singularly perturbed parabolic equations with the use of~dynamic~adapted meshes
\jour Model. Anal. Inform. Sist.
\yr 2016
\vol 23
\issue 3
\pages 334--341
\mathnet{http://mi.mathnet.ru/mais503}
\crossref{https://doi.org/10.18255/1818-1015-2016-3-334-341}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3520855}
\elib{http://elibrary.ru/item.asp?id=26246299}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. A. Davydova, N. N. Nefedov, “Existence and Stability of Contrast Structures in Multidimensional Singularly Perturbed Reaction-Diffusion-Advection Problems”, Numerical Analysis and Its Applications, NAA 2016, Lecture Notes in Computer Science, 10187, eds. I. Dimov, I. Farago, L. Vulkov, Springer International Publishing Ag, 2017, 277–285  crossref  mathscinet  zmath  isi  scopus
    2. A. Melnikova, N. Levashova, D. Lukyanenko, “Front Dynamics in An Activator-Inhibitor System of Equations”, Numerical Analysis and Its Applications, NAA 2016, Lecture Notes in Computer Science, 10187, eds. I. Dimov, I. Farago, L. Vulkov, Springer International Publishing Ag, 2017, 492–499  crossref  mathscinet  zmath  isi  scopus
    3. N. T. Levashova, N. N. Nefedov, A. V. Yagremtsev, “Existence of a solution in the form of a moving front of a reaction-diffusion-advection problem in the case of balanced advection”, Izv. Math., 82:5 (2018), 984–1005  mathnet  crossref  crossref  adsnasa  isi  elib
    4. A. A. Melnikova, N. N. Derugina, “The dynamics of the autowave front in a model of urban ecosystems”, Mosc. Univ. Phys. Bull., 73:3 (2018), 284–292  crossref  isi  scopus
    5. D. V. Lukyanenko, M. A. Shishlenin, V. T. Volkov, “Solving of the coefficient inverse problems for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time data”, Commun. Nonlinear Sci. Numer. Simul., 54 (2018), 233–247  crossref  mathscinet  isi  scopus
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