  The description of extreme-mass-ratio binary systems in the inspiral phase is
a challenging problem in gravitational wave physics with significant relevance
for the space interferometer LISA. The main difficulty lies in the evaluation
of the effects of the small body's gravitational field on itself. To that end,
an accurate computation of the perturbations produced by the small body with
respect the background geometry of the large object, a massive black hole, is
required. In this paper we present a new computational approach based on Finite
Element Methods to solve the master equations describing perturbations of
non-rotating black holes due to an orbiting point-like object. The numerical
computations are carried out in the time domain by using evolution algorithms
for wave-type equations. We show the accuracy of the method by comparing our
calculations with previous results in the literature. Finally, we discuss the
relevance of this method for achieving accurate descriptions of
extreme-mass-ratio binaries.
