HMG -- Homogeneous multigrid for HDG

Abstract

We introduce a homogeneous multigrid method in the sense that it uses the same HDG discretization scheme for Poisson's equation on all levels. In particular, we construct a stable injection operator and prove optimal convergence of the method under the assumption of elliptic regularity. Numerical experiments underline our analytical findings.

References in corpus (6)

• High order exactly divergence-free Hybrid Discontinuous Galerkin Methods for unsteady incompressible flows
• A Robust Multilevel Method for Hybridizable Discontinuous Galerkin Method for the Helmholtz Equation
• Hybrid discontinuous Galerkin discretisation and domain decomposition preconditioners for the Stokes problem
• Analysis of a two-level algorithm for HDG methods for diffusion problems
• Local Fourier analysis of multigrid for hybridized and embedded discontinuous Galerkin methods
• Locking free and gradient robust H(div)-conforming HDG methods for linear elasticity

Cited by in corpus (2)

• Analysis of injection operators in multigrid solvers for hybridized discontinuous Galerkin methods
• Homogeneous multigrid for embedded discontinuous Galerkin methods