  Interpreting gravitational wave observations and understanding the physics of
astrophysical compact objects such as black holes or neutron stars requires
accurate theoretical models. Here, we present a new numerical relativity
computer program, called Nmesh, that has the design goal to become a next
generation program for the simulation of challenging relativistic astrophysics
problems such as binary black hole or neutron star mergers. In order to
efficiently run on large supercomputers, Nmesh uses a discontinuous Galerkin
method together with a domain decomposition and mesh refinement that
parallelizes and scales well. In this work, we discuss the various numerical
methods we use. We also present results of test problems such as the evolution
of scalar waves, single black holes and neutron stars, as well as shock tubes.
In addition, we introduce a new positivity limiter that allows us to stably
evolve single neutron stars without an additional artificial atmosphere, or
other more traditional limiters.
