We propose a multigrid method to solve the linear system of equations arising from a hybrid discontinuous Galerkin (in particular, a single face hybridizable, a hybrid Raviart–Thomas, or a hybrid Brezzi–Douglas–Marini) discretization of a Stokes problem. Our analysis is centered around the augmented Lagrangian approach and we prove uniform convergence in this setting. Beyond this, we establish relations, which resemble those in Cockburn & Gopalakrishnan (2008, Error analysis of variable degree mixed methods for elliptic problems via hybridization. Math. Comput., 74, 1653–1677) for elliptic problems, between the approximates that are obtained by the single-face hybridizable, hybrid Raviart–Thomas and hybrid Brezzi–Douglas–Marini methods. Numerical experiments underline our analytical findings.

中文翻译：

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HDG 的均匀多重网格应用于 Stokes 方程

我们提出了一种多重网格方法来求解由斯托克斯问题的混合不连续伽辽金（特别是单面杂交、混合 Raviart-Thomas 或混合 Brezzi-Douglas-Marini）离散化产生的线性方程组。我们的分析以增强拉格朗日方法为中心，并证明了在这种情况下的一致收敛。除此之外，我们还建立了类似于 Cockburn & Gopalakrishnan (2008, Error Analysis ofvariable Degree MixedMethods for Elliptic Problems via Hybridization. Math.Comput., 74, 1653–1677) 中椭圆问题的近似值之间的关系：通过单面杂交、混合 Raviart-Thomas 和混合 Brezzi-Douglas-Marini 方法获得。数值实验强调了我们的分析结果。