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.
Mots-clés : error estimates, discontinuous time-stepping Galerkin schemes, FitzHugh-Nagumo equations, reaction-diffusion, parameter dependent, coarse time-stepping
@article{M2AN_2013__47_1_281_0,
author = {Chrysafinos, Konstantinos and Filopoulos, Sotirios P. and Papathanasiou, Theodosios K.},
title = {Error estimates for a {FitzHugh-Nagumo} parameter-dependent reaction-diffusion system},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {281--304},
publisher = {EDP-Sciences},
volume = {47},
number = {1},
year = {2013},
doi = {10.1051/m2an/2012028},
mrnumber = {2997502},
zbl = {1272.65072},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2012028/}
}
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 PY - 2013 SP - 281 EP - 304 VL - 47 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2012028/ DO - 10.1051/m2an/2012028 LA - en ID - M2AN_2013__47_1_281_0 ER -
%0 Journal Article %A Chrysafinos, Konstantinos %A Filopoulos, Sotirios P. %A Papathanasiou, Theodosios K. %T Error estimates for a FitzHugh-Nagumo parameter-dependent reaction-diffusion system %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2013 %P 281-304 %V 47 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2012028/ %R 10.1051/m2an/2012028 %G en %F M2AN_2013__47_1_281_0
Chrysafinos, Konstantinos; Filopoulos, Sotirios P.; Papathanasiou, Theodosios K. Error estimates for a FitzHugh-Nagumo parameter-dependent reaction-diffusion system. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 1, pp. 281-304. doi : 10.1051/m2an/2012028. http://www.numdam.org/articles/10.1051/m2an/2012028/
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