English

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}
}