A Virtual Element Method for a Nonlocal FitzHugh-Nagumo Model of Cardiac Electrophysiology
Provides a numerical method for simulating cardiac electrophysiology on general polygonal meshes, but the contribution is incremental as it extends existing VEM techniques to a specific model.
The paper develops a Virtual Element Method for a nonlocal FitzHugh-Nagumo model of cardiac electrophysiology, proving convergence and optimal-order error estimates, with numerical tests confirming the theory.
We present a Virtual Element Method (VEM) for a nonlocal reaction-diffusion system of the cardiac electric field. To this system, we analyze an $H^1(Ω)$-conforming discretization by means of VEM which can make use of general polygonal meshes. Under standard assumptions on the computational domain, we establish the convergence of the discrete solution by considering a series of a priori estimates and by using a general $L^p$ compactness criterion. Moreover, we obtain optimal order space-time error estimates in the $L^2$ norm. Finally, we report some numerical tests supporting the theoretical results.