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

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,...

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Bibliographic Details
Published in:ESAIM. Mathematical modelling and numerical analysis 2013-01, Vol.47 (1), p.281-304
Main Authors: Chrysafinos, Konstantinos, Filopoulos, Sotirios P., Papathanasiou, Theodosios K.
Format: Article
Language:English
Subjects:
35Q92
65M60
92-08
Algebra
Algebraic geometry
Approximation
coarse time-stepping
discontinuous time-stepping Galerkin schemes
Error analysis
Error estimates
Errors
Estimates
Exact sciences and technology
FitzHugh–Nagumo equations
Joining
Mathematical analysis
Mathematical models
Mathematics
Norms
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Numerical methods in probability and statistics
parameter dependent
Partial differential equations
reaction-diffusion
Regularity
Sciences and techniques of general use
Spacetime
Studies
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Summary: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.
ISSN:0764-583X
1290-3841
DOI:10.1051/m2an/2012028