  We describe an implicit general relativistic hydrodynamics code. The
evolution equations are formulated in comoving coordinates. A conservative
finite differencing of the Einstein equations is outlined, and artificial
viscosity and numerical diffusion are discussed. The time integration is
performed with AGILE, an implicit solver for stiff algebrodifferential
equations on a dynamical adaptive grid. We extend the adaptive grid technique,
known from nonrelativistic hydrodynamics, to the general relativistic
application and identify it with the concept of shift vectors in a 3+1
decomposition. The adaptive grid minimizes the number of required computational
zones without compromising the resolution in physically important regions.
Thus, the computational effort is greatly reduced when the zones are subject to
computationally expensive additional processes, such as Boltzmann radiation
transport or a nuclear reaction network. We present accurate results in the
standard tests for supernova simulations: Sedov's point-blast explosion, the
nonrelativistic and relativistic shock tube, the Oppenheimer-Snyder dust
collapse, and homologous collapse.
