  We present three-dimensional simulations of Einstein equations implementing a
symmetric hyperbolic system of equations with dynamical lapse. The numerical
implementation makes use of techniques that guarantee linear numerical
stability for the associated initial-boundary value problem. The code is first
tested with a gauge wave solution, where rather larger amplitudes and for
significantly longer times are obtained with respect to other state of the art
implementations. Additionally, by minimizing a suitably defined energy for the
constraints in terms of free constraint-functions in the formulation one can
dynamically single out preferred values of these functions for the problem at
hand. We apply the technique to fully three-dimensional simulations of a
stationary black hole spacetime with excision of the singularity, considerably
extending the lifetime of the simulations.

General Relativity and Quantum Cosmology