Analysis of injection operators in geometric multigrid solvers for HDG methods
Uniform convergence of the geometric multigrid V-cycle is proven for hybridized discontinuous Galerkin methods with a new set of assumptions on the injection operators from coarser to finer meshes. The scheme involves standard smoothers and local solvers which are bounded, convergent, and consistent...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
23 August 2022
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| In: |
SIAM journal on numerical analysis
Year: 2022, Volume: 60, Issue: 4, Pages: 2293-2317 |
| ISSN: | 1095-7170 |
| DOI: | 10.1137/21M1400110 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1137/21M1400110 Verlag, lizenzpflichtig, Volltext: https://epubs.siam.org/doi/10.1137/21M1400110 
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| Author Notes: | Peipei Lu, Andreas Rupp, and Guido Kanschat |
| Summary: | Uniform convergence of the geometric multigrid V-cycle is proven for hybridized discontinuous Galerkin methods with a new set of assumptions on the injection operators from coarser to finer meshes. The scheme involves standard smoothers and local solvers which are bounded, convergent, and consistent. A weak version of elliptic regularity is used in the proofs. The new assumptions admit injection operators local to each coarse grid cell. Examples for admissible injection operators are given. The analysis applies to the hybridized local discontinuous Galerkin method, hybridized Raviart--Thomas, and hybridized Brezzi--Douglas--Marini mixed element methods. Numerical experiments are provided to confirm the theoretical results. |
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| Item Description: | Gesehen am 20.10.2022 |
| Physical Description: | Online Resource |
| ISSN: | 1095-7170 |
| DOI: | 10.1137/21M1400110 |