We present a hybridizable discontinuous Galerkin (HDG) method for dissimilar meshes. The method is devised by formulating HDG discretizations on separate meshes and gluing these HDG discretizations through appropriate transmission conditions that weakly enforce the continuity of the numerical trace and the numerical flux across the dissimilar interfaces. The transmission conditions are based upon transferring the numerical flux from the first mesh to the second mesh and the numerical trace from the second mesh to the first one. The transfer of the numerical trace/flux from one mesh to the other relies on the extrapolation of the approximate flux, and is made to be consistent with the HDG methodology for conforming meshes. Stability of the HDG method is shown and the error analysis of the HDG method is established. Numerical results are presented to validate the theoretical results.

中文翻译：

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一种不同网格的 HDG 方法

我们提出了一种用于不同网格的可混合不连续 Galerkin (HDG) 方法。该方法是通过在单独的网格上制定 HDG 离散化并通过适当的传输条件粘合这些 HDG 离散化来设计的，这些传输条件弱强制数值轨迹的连续性和跨不同界面的数值通量。传输条件基于将数值通量从第一个网格传递到第二个网格以及将数值轨迹从第二个网格传递到第一个网格。数值轨迹/通量从一个网格到另一个网格的转移依赖于近似通量的外推，并且与用于一致网格的 HDG 方法一致。显示了HDG方法的稳定性，并建立了HDG方法的误差分析。