We consider Isogeometric Analysis in the framework of the Galerkin method for the spatial approximation
of cardiac electrophysiology models defined on NURBS surfaces; specifically, we perform a numerical comparison
between basis functions of degree p ≥ 1 and globally C
k
-continuous, with k = 0 or p − 1, to find
the most accurate approximation of a propagating front with the minimal number of degrees of freedom.
We show that B-spline basis functions of degree p ≥ 1, which are C
p−1
-continuous capture accurately the
front velocity of the transmembrane potential even with moderately refined meshes; similarly, we show that,
for accurate tracking of curved fronts, high-order continuous B-spline basis functions should be used. Finally,
we apply Isogeometric Analysis to an idealized human left atrial geometry described by NURBS with
physiologically sound fiber directions and anisotropic conductivity tensor to demonstrate that the numerical
scheme retains its favorable approximation properties also in a more realistic setting