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This work compares two Nitsche-type approaches to treat non-conformingtriangulations for a high-order discontinuous Galerkin (DG) solver for theacoustic conservation equations. The first approach (point-to-pointinterpolation) uses inexact integration with quadrature points prescribed by aprimary element. The second approach uses exact integration (mortaring) bychoosing quadratures depending on the intersection between non-conformingelements. In literature, some excellent properties regarding performance andease of implementation are reported for point-to-point interpolation. However,we show that this approach can not safely be used for DG discretizations of theacoustic conservation equations since, in our setting, it yields spuriousoscillations that lead to instabilities. This work presents a test case in thatwe can observe the instabilities and shows that exact integration is requiredto maintain a stable method. Additionally, we provide a detailed analysis ofthe method with exact integration. We show optimal spatial convergence ratesglobally and in each mesh region separately. The method is constructed suchthat it can natively treat overlaps between elements. Finally, we highlight thebenefits of non-conforming discretizations in acoustic computations by anumerical test case with different fluids.

High-Order Non-Conforming Discontinuous Galerkin Methods for the Acoustic Conservation Equations