# 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 (2012)

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

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topChrysafinos, 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 47.1 (2012): 281-304. <http://eudml.org/doc/244360>.

@article{Chrysafinos2012,

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},

keywords = {Error estimates; discontinuous time-stepping Galerkin schemes; FitzHugh–Nagumo equations; reaction-diffusion; parameter dependent; coarse time-stepping; FitzHugh-Nagumo equations; reaction-diffusion system; error estimates; Galerkin schemes; discontinuous time-stepping; stability; convergence},

language = {eng},

month = {11},

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/244360},

volume = {47},

year = {2012},

}

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

DA - 2012/11//

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; error estimates; Galerkin schemes; discontinuous time-stepping; stability; convergence

UR - http://eudml.org/doc/244360

ER -

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