In two and three dimension we analyze discontinuous Galerkin methods for the acoustic problem. The acoustic fluid that we consider on this paper is inviscid, leading to a linear eigenvalue problem. The acoustic problem is written, in first place, in terms of the displacement. Under the approach of the non-compact operators theory, we prove convergence and error estimates for the method when the displacement formulation is considered. We analyze the influence of the stabilization parameter on the computation of the spectrum, where spurious eigenmodes arise when this parameter is not correctly chosen. Alternatively we present the formulation depending only on the pressure, comparing the performance of the DG methods with the pure displacement formulation. Computationally, we study the influence of the stabilization parameter on the arising of spurious eigenvalues when the spectrum is computed. Also, we report tests in two and three dimensions where convergence rates are reported, together with a comparison between the displacement and pressure formulations for the proposed DG methods.

翻译：在两个和三个维度中,我们分析对声学问题的不连续的Galerkin方法。 我们在本文中考虑的声学流体是模糊的,导致线性二次值问题。 声学问题首先从迁移的角度写出来。 在非对称操作者理论的论调下, 我们证明在考虑离位配方时, 方法的趋同和误差估计。 我们分析稳定参数对频谱计算的影响, 当该参数没有正确选择时, 会出现虚假的双元模型。 或者, 我们只根据压力来显示配方, 比较DG方法的性能和纯流离位配方。 计算频谱时, 我们比较了稳定参数对浮性双维值的影响。 此外, 我们报告在两个维度的测试, 并同时比较拟议的D方法的离位和压力配方。