  We consider the damped time-harmonic Galbrun's equation, which is used to
model stellar oscillations. We introduce a discontinuous Galerkin finite
element method (DGFEM) with $H(\operatorname{div})$-elements, which is
nonconform with respect to the convection operator. We report a convergence
analysis, which is based on the frameworks of discrete approximation schemes
and T-compatibility. A novelty is that we show how to interprete a DGFEM as a
discrete approximation scheme and this approach enables us to apply compact
perturbation arguments in a DG-setting, and to circumvent any extra regularity
assumptions on the solution. The advantage of the proposed
$H(\operatorname{div})$-DGFEM compared to $H^1$-conforming methods is that we
do not require a minimal polynomial order or any special assumptions on the
mesh structure. The considered DGFEM is constructed without a stabilization
term, which considerably improves the assumption on the smallness of the Mach
number compared to other DG methods and $H^1$-conforming methods, and the
obtained bound is fairly explicit. In addition, the method is robust with
respect to the drastic changes of magnitude of the density and sound speed,
which occur in stars. The convergence of the method is obtained without
additional regularity assumptions on the solution, and for smooth solutions and
parameters convergence rates are derived.
