HDG and HDG+ methods for harmonic wave problems with convection

In this report, we introduce three variants of the HDG method based on two weak formulations of the convected Helmholtz equation. Two of them are standard HDG methods with the same interpolation degree for all the unknowns and one of them uses a higher interpolation degree for the volumetric scalar un- known. For those three numerical methods, a detailed analysis including local and global well-posedness, as well as convergence estimates is carried out. We then pro- vide implementation details and numerical experiments to illustrate our theoretical results.