The bidomain model of electrical activity of myocardial
tissue consists of a possibly degenerate parabolic PDE
coupled with an elliptic PDE for the transmembrane and
extracellular potentials, respectively. This system of
two scalar PDEs is supplemented by a time-dependent ODE
modeling the evolution of the gating variable. In the
simpler sub-case of the monodomain model, the elliptic
PDE reduces to an algebraic equation. Since typical
solutions of the bidomain and monodomain models exhibit
wavefronts with steep gradients, we propose a finite
volume scheme enriched by a fully adaptive
multiresolution method, whose basic purpose is to
concentrate computational effort on zones of strong
variation of the solution. Time adaptivity is achieved by
two alternative devices, namely locally varying time
stepping and a Runge-Kutta-Fehlberg-type adaptive time
integration. A series of numerical examples demonstrates
that these methods are efficient and sufficiently
accurate to simulate the electrical activity in
myocardial tissue with affordable effort. In addition,
the optimal choice of the threshold for discarding
non-significant information in the multiresolution
representation of the solution is addressed, and the
numerical efficiency and accuracy of the method is
measured in terms of CPU time speed-up, memory
compression, and errors in different norms.