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
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.
singularly perturbed parabolic periodic problems, interior layer, Shishkin mesh, dynamic adapted mesh.
|Russian Foundation for Basic Research
|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.
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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
\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.
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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
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
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
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
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
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