  Simulations of relativistic hydrodynamics often need both high accuracy and
robust shock-handling properties. The discontinuous Galerkin method combines
these features --- a high order of convergence in regions where the solution is
smooth and shock-capturing properties for regions where it is not --- with
geometric flexibility and is therefore well suited to solve the partial
differential equations describing astrophysical scenarios. We present here
evolutions of a general-relativistic neutron star with the discontinuous
Galerkin method. In these simulations, we simultaneously evolve the spacetime
geometry and the matter on the same computational grid, which we conform to the
spherical geometry of the problem. To verify the correctness of our
implementation, we perform standard convergence and shock tests. We then show
results for evolving, in three dimensions, a Kerr black hole; a neutron star in
the Cowling approximation (holding the spacetime metric fixed); and, finally, a
neutron star where the spacetime and matter are both dynamical. The evolutions
show long-term stability, good accuracy, and an improved rate of convergence
versus a comparable-resolution finite-volume method.
