Error estimates for a FitzHugh-Nagumo parameter-dependent reaction-diffusion system
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 47 (2013) no. 1, p. 281-304

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.

DOI : https://doi.org/10.1051/m2an/2012028
Classification:  65M60,  35Q92,  92-08
Keywords: 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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {47},
     number = {1},
     year = {2013},
     pages = {281-304},
     doi = {10.1051/m2an/2012028},
     zbl = {1272.65072},
     mrnumber = {2997502},
     language = {en},
     url = {http://www.numdam.org/item/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 - Modélisation Mathématique et Analyse Numérique, Volume 47 (2013) no. 1, pp. 281-304. doi : 10.1051/m2an/2012028. http://www.numdam.org/item/M2AN_2013__47_1_281_0/

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