Error estimates for a FitzHugh-Nagumo parameter-dependent reaction-diffusion system (Q2836464)

The FitzHugh-Nagumo (FHN) system, which consists of two parabolic partial differential equations that are coupled through nonlinear terms were proposed for the modeling of the transmission of electrical impulses in a nerve axon (see, e.g. [\textit{R. FitzHugh}, Biophys. J. 1, 445--466 (1961)]). A space-time approximation of the FHN system is studied here (cf. [\textit{K. Chrysafinos} et al., ESAIM, Math. Model. Numer. Anal. 42, No. 1, 25--55 (2008; Zbl 1136.65089)]). The object of the authors is to derive stability and error estimates of arbitrary order for which time discretization and spatial discretization parameters can be chosen independently. Convergence under minimal regularity assumptions on the given data are demonstrated. Optimal error estimates are derived when the solutions are sufficiently smooth.