Multigrid methods for Hdiv-conforming discontinuous Galerkin methods for the Stokes equations

• Verfasst von: Kanschat, Guido [VerfasserIn]
• Verfasst von: Mao, Youli [VerfasserIn]
• Titel: Multigrid methods for Hdiv-conforming discontinuous Galerkin methods for the Stokes equations
• Verf.angabe: Guido Kanschat and Youli Mao
• Umfang: 16 S.
• Fussnoten: Im Titel ist die Zeichenfolge div hochgestellt. ; Gesehen am 23.01.2018
• Titel Quelle: Enthalten in: Journal of numerical mathematics
• Jahr Quelle: 2015
• Band/Heft Quelle: 23(2015), 1, S. 51-66
• ISSN Quelle: 1569-3953
• DOI: doi:10.1515/jnma-2015-0005
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1567496644

Abstract

A multigrid method for the Stokes system discretized with an Hdiv-conforming discontinuous Galerkin method is presented. It acts on the combined velocity and pressure spaces and thus does not need a Schur complement approximation. The smoothers used are of overlapping Schwarz type and employ a local Helmholtz decomposition. Additionally, we use the fact that the discretization provides nested divergence free subspaces. We present the convergence analysis and numerical evidence that convergence rates are not only independent of mesh size, but also reasonably small.