Homogeneous multigrid for embedded discontinuous Galerkin methods

TL;DR

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

Contribution

It introduces a multigrid approach that employs the same EDG scheme on all levels, ensuring optimal convergence for Poisson's equation.

Findings

Optimal convergence proven under elliptic regularity.

Numerical experiments confirm analytical results.

Abstract

We introduce a homogeneous multigrid method in the sense that it uses the same embedded discontinuous Galerkin (EDG) discretization scheme for Poisson's equation on all levels. In particular, we use the injection operator developed in [LuRK2020] for HDG and prove optimal convergence of the method under the assumption of elliptic regularity. Numerical experiments underline our analytical findings.