  In this paper, we will consider an $hp$-finite elements discretization of a
highly indefinite Helmholtz problem by some dG formulation which is based on
the ultra-weak variational formulation by Cessenat and Depr\'{e}s. We will
introduce an a posteriori error estimator and derive reliability and efficiency
estimates which are explicit with respect to the wavenumber and the
discretization parameters $h$ and $p$. In contrast to the conventional
conforming finite element method for indefinite problems, the dG formulation is
unconditionally stable and the adaptive discretization process may start from a
very coarse initial mesh. Numerical experiments will illustrate the efficiency
and robustness of the method.
