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

Published online by Cambridge University Press:  23 November 2012

Konstantinos Chrysafinos ,
Sotirios P. Filopoulos  and
Theodosios K. Papathanasiou
Konstantinos Chrysafinos
Affiliation:
Department of Mathematics, National Technical University of Athnens, Zografou Campus, 15780 Athens, Greece. chrysafinos@math.ntua.gr
Sotirios P. Filopoulos
Affiliation:
Section of Applied and Theoretical Mechanics, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece; sfilop@gmail.com; papathth@gmail.com
Theodosios K. Papathanasiou
Affiliation:
Section of Applied and Theoretical Mechanics, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece; sfilop@gmail.com; papathth@gmail.com
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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.

Keywords

Error estimatesdiscontinuous time-stepping Galerkin schemesFitzHugh–Nagumo equationsreaction-diffusionparameter dependentcoarse time-stepping
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 1 , January 2013 , pp. 281 - 304
Copyright
© EDP Sciences, SMAI, 2012

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