Error estimates for a FitzHugh–Nagumo parameter-dependent reaction-diffusion system

Konstantinos Chrysafinos; Sotirios P. Filopoulos; Theodosios K. Papathanasiou

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2013)

  • Volume: 47, Issue: 1, page 281-304
  • ISSN: 0764-583X

Abstract

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Space-time approximations of the FitzHugh–Nagumo system of coupled semi-linear parabolic PDEs are examined. The schemes under consideration are discontinuous in time but conforming in space and of arbitrary order. Stability estimates are presented in the natural energy norms and at arbitrary times, under minimal regularity assumptions. Space-time error estimates of arbitrary order are derived, provided that the natural parabolic regularity is present. Various physical parameters appearing in the model are tracked and numerical examples are presented.

How to cite

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Chrysafinos, Konstantinos, Filopoulos, Sotirios P., and Papathanasiou, Theodosios K.. "Error estimates for a FitzHugh–Nagumo parameter-dependent reaction-diffusion system." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.1 (2013): 281-304. <http://eudml.org/doc/273288>.

@article{Chrysafinos2013,
abstract = {Space-time approximations of the FitzHugh–Nagumo system of coupled semi-linear parabolic PDEs are examined. The schemes under consideration are discontinuous in time but conforming in space and of arbitrary order. Stability estimates are presented in the natural energy norms and at arbitrary times, under minimal regularity assumptions. Space-time error estimates of arbitrary order are derived, provided that the natural parabolic regularity is present. Various physical parameters appearing in the model are tracked and numerical examples are presented.},
author = {Chrysafinos, Konstantinos, Filopoulos, Sotirios P., Papathanasiou, Theodosios K.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {error estimates; discontinuous time-stepping Galerkin schemes; FitzHugh–Nagumo equations; reaction-diffusion; parameter dependent; coarse time-stepping; FitzHugh-Nagumo equations; reaction-diffusion system; Galerkin schemes; discontinuous time-stepping; stability; convergence},
language = {eng},
number = {1},
pages = {281-304},
publisher = {EDP-Sciences},
title = {Error estimates for a FitzHugh–Nagumo parameter-dependent reaction-diffusion system},
url = {http://eudml.org/doc/273288},
volume = {47},
year = {2013},
}

TY - JOUR
AU - Chrysafinos, Konstantinos
AU - Filopoulos, Sotirios P.
AU - Papathanasiou, Theodosios K.
TI - Error estimates for a FitzHugh–Nagumo parameter-dependent reaction-diffusion system
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2013
PB - EDP-Sciences
VL - 47
IS - 1
SP - 281
EP - 304
AB - Space-time approximations of the FitzHugh–Nagumo system of coupled semi-linear parabolic PDEs are examined. The schemes under consideration are discontinuous in time but conforming in space and of arbitrary order. Stability estimates are presented in the natural energy norms and at arbitrary times, under minimal regularity assumptions. Space-time error estimates of arbitrary order are derived, provided that the natural parabolic regularity is present. Various physical parameters appearing in the model are tracked and numerical examples are presented.
LA - eng
KW - error estimates; discontinuous time-stepping Galerkin schemes; FitzHugh–Nagumo equations; reaction-diffusion; parameter dependent; coarse time-stepping; FitzHugh-Nagumo equations; reaction-diffusion system; Galerkin schemes; discontinuous time-stepping; stability; convergence
UR - http://eudml.org/doc/273288
ER -

References

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