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We consider interior penalty discontinuous Galerkin discretizations oftime-harmonic wave propagation problems modeled by the Helmholtz equation, andderive novel a priori and a posteriori estimates. Our analysis classicallyrelies on duality arguments of Aubin-Nitsche type, and its originality is thatit applies under minimal regularity assumptions. The estimates we obtaindirectly generalize known results for conforming discretizations, namely thatthe discrete solution is optimal in a suitable energy norm and that the errorcan be explicitly controlled by a posteriori estimators, provided the mesh issufficiently fine.

Duality analysis of interior penalty discontinuous Galerkin methods  under minimal regularity and application to the a priori and a posteriori  error analysis of Helmholtz problems