HMG -- Homogeneous multigrid for HDG

TL;DR

This paper presents a homogeneous multigrid method for solving Poisson's equation using the same HDG discretization across all levels, demonstrating optimal convergence and validated by numerical experiments.

Contribution

It introduces a stable injection operator and proves the optimal convergence of a multigrid method that employs a uniform HDG discretization scheme.

Findings

Optimal convergence proven under elliptic regularity

Numerical experiments confirm theoretical results

Stable injection operator constructed for multigrid levels

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.