Homogeneous Multigrid for Hybrid Discretizations: Application to HHO Methods
ABSTRACT 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.
Authors
- Andreas Norbert Rupp (ORCID: https://orcid.org/0000-0001-5527-7187)
- Daniele A. Di Pietro (ORCID: https://orcid.org/0000-0003-0959-8830)
- Guido Kanschat (ORCID: https://orcid.org/0000-0003-1687-7328)
- Pierre Matalon (ORCID: https://orcid.org/0000-0002-4288-2289)
- Zhaonan Dong (ORCID: https://orcid.org/0000-0003-4083-6593)
Institutions
- Centre National de la Recherche Scientifique (FR)
- École Polytechnique (FR)
- Université de Montpellier (FR)
- Heidelberg University (DE)
- Centre de Mathématiques Appliquées de l'École polytechnique (FR)
- CERMICS (FR)
- Lappeenranta-Lahti University of Technology (FI)
- Saarland University (DE)
Publication Details
- Journal
- Numerical Methods for Partial Differential Equations
- Published
- 2025-08-05
- DOI
- https://doi.org/10.1002/num.70023
- Citations
- 1
- Primary Topic
- Advanced Numerical Methods in Computational Mathematics
- Type
- article
- Field-Weighted Citation Impact
- 1.33
Funders
- European Commission
- Deutsche Forschungsgemeinschaft
- Academy of Finland
- Business Finland
- H2020 European Research Council