Homogeneous multigrid for HDG applied to the Stokes equation

• Verfasst von: Lu, Peipei [VerfasserIn]
• Verfasst von: Wang, Wei [VerfasserIn]
• Verfasst von: Kanschat, Guido [VerfasserIn]
• Verfasst von: Rupp, Andreas [VerfasserIn]
• Titel: Homogeneous multigrid for HDG applied to the Stokes equation
• Verf.angabe: Peipei Lu, Wei Wang, Guido Kanschat and Andreas Rupp
• E-Jahr: 2023
• Jahr: Oct 2023
• Umfang: 29 S.
• Fussnoten: Gesehen am 14.05.2024
• Titel Quelle: Enthalten in: Institute of Mathematics and Its ApplicationsIMA journal of numerical analysis
• Ort Quelle: Oxford : Oxford Univ. Press, 1981
• Jahr Quelle: 2023
• Band/Heft Quelle: (2023), Artikel-ID drad079, Seite 1-29
• ISSN Quelle: 1464-3642
• DOI: doi:10.1093/imanum/drad079
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1888472510

Abstract

We propose a multigrid method to solve the linear system of equations arising from a hybrid discontinuous Galerkin (in particular, a single face hybridizable, a hybrid Raviart-Thomas, or a hybrid Brezzi-Douglas-Marini) discretization of a Stokes problem. Our analysis is centered around the augmented Lagrangian approach and we prove uniform convergence in this setting. Beyond this, we establish relations, which resemble those in Cockburn & Gopalakrishnan (2008, Error analysis of variable degree mixed methods for elliptic problems via hybridization. Math. Comput., 74, 1653-1677) for elliptic problems, between the approximates that are obtained by the single-face hybridizable, hybrid Raviart-Thomas and hybrid Brezzi-Douglas-Marini methods. Numerical experiments underline our analytical findings.