In this work, a novel analysis of a hybrid discontinuous Galerkin method for the Helmholtz equation is presented. It uses wavenumber, mesh size and polynomial degree independent stabilisation parameters leading to impedance traces between elements. With analysis techniques based on projection operators unique discrete solvability without a resolution condition and optimal convergence rates with respect to the mesh size are proven. The considered method is tailored towards enabling static condensation and the usage of iterative solvers.

翻译：本文提出了一种针对亥姆霍兹方程的混合间断伽辽金方法的新颖分析。该方法采用与波数、网格尺寸及多项式阶数无关的稳定化参数，从而在单元间引入阻抗迹线。基于投影算子的分析技术，证明了该方法在无需满足分辨率条件的情况下具有唯一的离散可解性，并实现了关于网格尺寸的最优收敛阶。所考虑的方法专门设计用于实现静态凝聚以及迭代求解器的使用。