Homogeneous multigrid for HDG applied to the Stokes equation

Author:

Lu Peipei1,Wang Wei2,Kanschat Guido3,Rupp Andreas4

Affiliation:

1. Department of Mathematics Sciences, Soochow University , Suzhou, 215006, China

2. LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing , Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

3. Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University , Mathematikon, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany

4. School of Engineering Science, Lappeenranta–Lahti University of Technology , P.O. Box 20, 53851 Lappeenranta, Finland

Abstract

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.

Publisher

Oxford University Press (OUP)

Subject

Applied Mathematics,Computational Mathematics,General Mathematics

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