Veronica Anaya, Mostafa Bendahmane, David Mora, Mauricio Sepúlveda:
A virtual element method for a nonlocal FitzHugh-Nagumo model of cardiac electrophysiology
We present a Virtual ElementMethod (VEM) for a nonlocal reaction-diffusion system of the cardiac electric field. To this system, we analyze an H1(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 Lp compactness criterion. Moreover, we obtain optimal order space-time error estimates in the L2 norm. Finally, we report some numerical tests supporting the theoretical results.