Homogeneous multigrid method for HDG applied to the Stokes equation

TL;DR

This paper introduces a multigrid solver tailored for hybrid discontinuous Galerkin discretizations of the Stokes equation, demonstrating uniform convergence through theoretical analysis and numerical validation.

Contribution

It presents a novel multigrid method specifically designed for HDG discretizations of the Stokes problem, with proven uniform convergence.

Findings

Proven uniform convergence of the multigrid method.

Numerical experiments confirm the theoretical results.

Effective solver for hybrid DG discretizations of Stokes.

Abstract

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. Numerical experiments underline our analytical findings.