  We present a new numerical dissipation algorithm, which can be efficiently
used in combination with centered finite-difference methods. We start from a
formulation of centered finite-volume methods for Numerical Relativity, in
which third-order space accuracy can be obtained by employing just
piecewise-linear reconstruction. We obtain a simplified version of the
algorithm, which can be viewed as a centered finite-difference method plus some
'adaptive dissipation'. The performance of this algorithm is confirmed by
numerical results obtained from 3D black hole simulations.
