Convergence Analysis for Virtual Element Discretizations of the Cardiac Bidomain Model

We propose here a convergence analysis for virtual element discretizations of the cardiac Bidomain model, a degenerate system of parabolic reaction-diffusion equations that models the propagation of the electric signal in the cardiac tissue. The virtual element method is a recent numerical technology that generalizes finite elements by considering polytopal computational grids, thus allowing more flexibility and accuracy in approximating complex computational domains. This can be an advantage when modeling for instance damaged cardiac tissues or structural heterogeneities. A previous similar study was performed in Anaya et al. (IMA J Numer Anal 40(2):1544–1576, 2020), where the propagation was modeled by means of a scalar nonlocal FitzHugh-Nagumo reaction-diffusion model. In the present work, we extend this analysis to the full semi-discrete Bidomain system, providing extensive numerical tests that validate the theoretical result on several structured and unstructured meshes.