Local Fourier analysis of multigrid for hybridized and embedded discontinuous Galerkin methods
Numerical Analysis
2023-07-07 v1 Numerical Analysis
Abstract
In this paper we present a geometric multigrid method with Jacobi and Vanka relaxation for hybridized and embedded discontinuous Galerkin discretizations of the Laplacian. We present a local Fourier analysis (LFA) of the two-grid error-propagation operator and show that the multigrid method applied to an embedded discontinuous Galerkin (EDG) discretization is almost as efficient as when applied to a continuous Galerkin discretization. We furthermore show that multigrid applied to an EDG discretization outperforms multigrid applied to a hybridized discontinuous Galerkin (HDG) discretization. Numerical examples verify our LFA predictions.
Keywords
Cite
@article{arxiv.2006.11433,
title = {Local Fourier analysis of multigrid for hybridized and embedded discontinuous Galerkin methods},
author = {Yunhui He and Sander Rhebergen and Hans De Sterck},
journal= {arXiv preprint arXiv:2006.11433},
year = {2023}
}