Homogeneous multigrid for HDG applied to the Stokes equation
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...
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| Main Authors: | , , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
Oct 2023
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| In: |
IMA journal of numerical analysis
Year: 2023, Pages: 1-29 |
| ISSN: | 1464-3642 |
| DOI: | 10.1093/imanum/drad079 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1093/imanum/drad079
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| Author Notes: | Peipei Lu, Wei Wang, Guido Kanschat and Andreas Rupp |
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| 520 | |a 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. | ||
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