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

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

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 1, pp. 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.

Classification : 65M60, 35Q92, 92-08
Mots clés : error estimates, discontinuous time-stepping Galerkin schemes, FitzHugh-Nagumo equations, reaction-diffusion, parameter dependent, coarse time-stepping

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