Geodesic
Analytic-numerical approach to solving singularly perturbed parabolic equations with the use of~dynamic~adapted meshes
Modelirovanie i analiz informacionnyh sistem, Tome 23 (2016) no. 3, pp. 334-341

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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. 
@article{MAIS_2016_23_3_a9,
     author = {D. V. Lukyanenko and V. T. Volkov and N. N. Nefedov and L. Recke and K. Schneider},
     title = {Analytic-numerical approach to solving singularly perturbed parabolic equations with the use of~dynamic~adapted meshes},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {334--341},
     publisher = {mathdoc},
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     number = {3},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2016_23_3_a9/}
}
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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. Modelirovanie i analiz informacionnyh sistem, Tome 23 (2016) no. 3, pp. 334-341. http://geodesic.mathdoc.fr/item/MAIS_2016_23_3_a9/