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On the a posteriori error analysis for linear Fokker–Planck models in convection-dominated diffusion problems

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  • Matculevich, Svetlana
  • Wolfmayr, Monika

Abstract

This work is aimed at the derivation of reliable and efficient a posteriori error estimates for convection-dominated diffusion problems motivated by a linear Fokker–Planck problem appearing in computational neuroscience. We obtain computable error bounds of functional type for the static and time-dependent case and for different boundary conditions (mixed and pure Neumann boundary conditions). Finally, we present a set of various numerical examples including discussions on mesh adaptivity and space-time discretisation. The numerical results confirm the reliability and efficiency of the error estimates derived.

Suggested Citation

  • Matculevich, Svetlana & Wolfmayr, Monika, 2018. "On the a posteriori error analysis for linear Fokker–Planck models in convection-dominated diffusion problems," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 779-804.
    • Handle: RePEc:eee:apmaco:v:339:y:2018:i:c:p:779-804
    DOI: 10.1016/j.amc.2018.05.050
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    References listed on IDEAS

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    1. Repin, Sergey I., 1999. "A unified approach to a posteriori error estimation based on duality error majorants," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 50(1), pages 305-321.
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