We design and analyze a coupling of a discontinuous Galerkin finite element method with a boundary element method to solve the Helmholtz equation with variable coefficients in three dimensions. The coupling is realized with a mortar variable that is related to an impedance trace on a smooth interface. The method obtained has a block structure with nonsingular subblocks. We prove quasi-optimality of the $h$- and $p$-versions of the scheme, under a threshold condition on the approximability properties of the discrete spaces. Amongst others, an essential tool in the analysis is a novel discontinuous-to-continuous reconstruction operator on tetrahedral meshes with curved faces.

翻译：我们设计并分析一种不连续的Galerkin定点元件方法与一种边界元件方法的结合,用三个维度的可变系数解决赫尔姆霍尔茨方程式。这种结合与一个迫击炮变量实现,该变量与光滑界面上的阻力追踪有关。获得的方法有一个与非单质子块块的块状结构。我们证明,在离散空间的接近性能临界条件下,该计划的美元-美元和美元-折价转换的准最佳性。除其他外,分析中的一个基本工具是,对面部弯曲的四面形金属进行新颖的不连续重建操作者。