SIAM Journal on Scientific Computing, Ahead of Print.
In this paper we present a geometric multigrid method with Jacobi and Vanka relaxation for hybridized and embedded discontinuous Galerkin discretizations of the Laplacian. We present a local Fourier analysis (LFA) of the two-grid error-propagation operator and show that the multigrid method applied to an embedded discontinuous Galerkin (EDG) discretization is almost as efficient as when applied to a continuous Galerkin discretization. We furthermore show that multigrid applied to an EDG discretization outperforms multigrid applied to a hybridized discontinuous Galerkin discretization. Numerical examples verify our LFA predictions.

中文翻译：

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混合和嵌入式不连续伽辽金方法的多重网格局部傅里叶分析

SIAM 科学计算杂志，提前印刷。
在本文中，我们提出了一种带有 Jacobi 和 Vanka 松弛的几何多重网格方法，用于拉普拉斯算子的混合和嵌入的不连续 Galerkin 离散化。我们提出了双网格误差传播算子的局部傅里叶分析 (LFA)，并表明应用于嵌入式不连续伽辽金 (EDG) 离散化的多重网格方法几乎与应用于连续伽辽金离散化时一样有效。我们进一步表明，应用于 EDG 离散化的多重网格优于应用于混合不连续 Galerkin 离散化的多重网格。数值例子验证了我们的 LFA 预测。