Abstract 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 (div) H (div) -elements, which is nonconforming 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 interpret 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 (div) H (div) -DGFEM compared to H¹ H 1 -conforming methods is that we do not require a minimal polynomial order or any special assumptions on the mesh structure. Further, we extend the analysis of the symmetric interior penalty DGFEM to a DGFEM without a penalty term, which considerably improves the smallness assumption on the Mach number to a fairly explicit bound. In addition, the method is robust with respect to the drastic changes of magnitude of the density and sound speed, which occur in stars.
Martin Halla (Mon,) studied this question.