Homogeneous multigrid for hybrid discretizations: application to HHO methods

Daniele A. Di Pietro (1) , Zhaonan Dong (2, 3) , Guido Kanschat (4) , Pierre Matalon (5) , Andreas Rupp (6)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 SERENA - Simulation for the Environment: Reliable and Efficient Numerical Algorithms
3 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
4 IWR - Interdisciplinary Center for Scientific Computing
5 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
6 School of Engineering Sciences [Lappeenranta]

We prove the uniform convergence of the geometric multigrid V- cycle for hybrid high-order (HHO) and other discontinuous skeletal methods. Our results generalize previously established results for HDG methods, and our multigrid method uses standard smoothers and local solvers that are bounded, convergent, and consistent. We use a weak version of elliptic regularity in our proofs. Numerical experiments confirm our theoretical results.

Mots clés: Geometric multigrid; Homogeneous multigrid; Hybrid high-order methods; Skeleton methods

Domaines: Mathématiques [math]

Daniele A. Di Pietro, Zhaonan Dong, Guido Kanschat, Pierre Matalon, Andreas Rupp. Homogeneous multigrid for hybrid discretizations: application to HHO methods. 2024. ⟨hal-04518103v1⟩