Uniform convergence of the geometric multigrid V-cycle is proven for HDG methods with a new set of assumptions on the injection operators from coarser to finer meshes. The scheme involves standard smoothers and local solvers which are bounded, convergent, and consistent. Elliptic regularity is used in the proofs. The new assumptions admit injection operators local to a single coarse grid cell. Examples for admissible injection operators are given. The analysis applies to the hybridized local discontinuous Galerkin method, hybridized Raviart-Thomas, and hybridized Brezzi-Douglas-Marini mixed element methods. Numerical experiments are provided to confirm the theoretical results.

翻译：对于HDG方法来说,几何多格多格V周期的统一一致已被证明与一套关于从粗体到细体的注射操作员的新假设相统一。这个办法涉及标准平滑器和当地溶剂,它们相互交织、趋同和一致。在证据中使用了椭圆规律性。新的假设将当地注射操作员纳入一个单一粗体格格中。提供了可允许注射操作员的例子。分析适用于当地混合的不连续加勒金方法、混合的拉维亚-托马斯和混合的布列兹齐-杜格拉斯-马里尼混合元素方法。提供了数字实验,以证实理论结果。