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

Abstract

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.Mathematics Subject Classification. 65M60, 35Q92, 92-08.

Riccati-Based Feedback Control of the Monodomain Equations With the Fitzhugh--Nagumo Model

“…Further numerical studies and error estimates Downloaded 05/14/15 to 130.132.123.28. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php are discussed in, e.g., [12,15,20]. In this paper, we consider the FitzHugh-Nagumo model, in the form…”

“…Optimal control of reaction-diffusion-type partial differential equations (PDEs) arising in cardiac electrophysiology has received considerable interest in the last few years; see, e.g., [11,12,15,19,20,22]. The so-called bidomain equations are a well-accepted model representing defibrillation processes of the human heart (see [36]).…”

A virtual element method for a nonlocal FitzHugh–Nagumo model of cardiac electrophysiology

“…Over the past years, some papers related to numerical tools for solving this model and its variations have appeared. For example, in [33] a continuous in space and discontinuous in time Galerkin method of arbitrary order has been developed, under minimal regularity assumptions, space-time error estimates are established in the natural norms. In [39] some estimates in the L 2 norm for semi-discrete Galerkin approximations for the FitzHugh-Nagumo model are derived.…”