According to the World Health Organization heart diseases are one of the
top ten causes of death in western society. This is one of the reasons
that the pursuit of knowledge about the human heart has gained more
importance, not only by a desire to understand the mechanical and
electrochemical processes, but also by the increasing clinical
importance. An important technique to establish more knowledge is
modeling. With this, one is able to describe the function of the human
heart with sets of time dependent highly nonlinear partial differential
equations. Due to its complicated nature, sophisticated solvers are
needed. In this work we will focus on the application of a fairly new
technique to solve such complex problems.

A classic way of
discretizing time dependent problems is to discretize first in space
with finite element techniques and, afterwards, use suitable time
stepping methods. In this work we will consider a different approach.
Instead of separating space and time we will apply discretization
techniques in both space and time. This allows for rather general almost
arbitrary discretizations of space-time geometries. Furthermore, this
approach opens the door for space-time parallel solver development.
Another advantage of this space-time discretization is the applicability
of adaptive algorithms to resolve physical properties better in space
and time simultaneously.