Use of Asymptotics for New Dynamic Adapted Mesh Construction for Periodic Solutions with an Interior Layer of Reaction-Diffusion-Advection Equations

  • Dmitry Lukyanenko
  • Nikolay NefedovEmail author
  • Egor Nikulin
  • Vladimir Volkov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10187)


This paper presents the development of analytic-numerical approaches to study periodically moving fronts in singularly perturbed reaction-diffusion-advection models. We describe the results of rigorous asymptotic treatment of the problem and suggest a method to generate a dynamic adapted mesh for the numerical solution of such problems. This method based on a priori information. In particular, we take into account a priori estimates on the location of the transition layer, its width and structure. An example is presented to demonstrate the effectiveness of the proposed method.


Singularly perturbed parabolic periodic problems Interior layer Shishkin mesh Dynamic adapted mesh 



The work was supported by RFBR (projects No. 17-01-00519, 17-01-00670, 17-01-00159, 16-01-00755 and 16-01-00437) and the Ministry of Education and Science of the Russian Federation.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Dmitry Lukyanenko
    • 1
  • Nikolay Nefedov
    • 1
    Email author
  • Egor Nikulin
    • 1
  • Vladimir Volkov
    • 1
  1. 1.Faculty of Physics, Department of MathematicsLomonosov Moscow State UniversityMoscowRussia

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