  This work aims at presenting a Discontinuous Galerkin (DG) formulation
employing a spectral basis for two important models employed in cardiac
electrophysiology, namely the monodomain and bidomain models. The use of DG
methods is motivated by the characteristic of the mathematical solution of such
equations which often corresponds to a highly steep wavefront. Hence, the
built-in flexibility of discontinuous methods in developing adaptive
approaches, combined with the high-order accuracy, can well represent the
underlying physics. The choice of a semi-implicit time integration allows for a
fast solution at each time step. The article includes some numerical tests to
verify the convergence properties and the physiological behaviour of the
numerical solution. Also, a pseudo-realistic simulation turns out to fully
reconstruct the propagation of the electric potential, comprising the phases of
depolarization and repolarization, by overcoming the typical issues related to
the steepness of the wave front.
