  This is a brief report on time-domain numerical simulations of
extreme-mass-ratio binaries based on finite element methods. We discuss a new
technique for solving the perturbative equations describing a point-like object
orbiting a non-rotating massive black hole and the prospects of using it for
the evaluation of the gravitational self-force responsible of the inspiral of
these binary systems. We also discuss the perspectives of transferring this
technology to the more astrophysically relevant case of a central rotating
massive black hole.
