Homogeneous multigrid for HDG applied to the Stokes equation - Lu, Peipei; Wang, Wei; Kanschat, Guido; Rupp, Andreas (IMA journal of numerical analysis, 2023)
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.