Adaptive multilevel methods with local smoothing for H1- and Hcurl-conforming high order finite element methods
A multilevel method on adaptive meshes with hanging nodes is presented, and the additional matrices appearing in the implementation are derived. Smoothers of overlapping Schwarz type are discussed; smoothing is restricted to the interior of the subdomains refined to the current level; thus it has op...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2011
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| In: |
SIAM journal on scientific computing
Year: 2011, Volume: 33, Issue: 4, Pages: 2095-2114 |
| ISSN: | 1095-7197 |
| DOI: | 10.1137/090778523 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1137/090778523 Verlag, lizenzpflichtig, Volltext: https://epubs.siam.org/doi/10.1137/090778523 
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| Author Notes: | Bärbel Janssen and Guido Kanschat |
| Summary: | A multilevel method on adaptive meshes with hanging nodes is presented, and the additional matrices appearing in the implementation are derived. Smoothers of overlapping Schwarz type are discussed; smoothing is restricted to the interior of the subdomains refined to the current level; thus it has optimal computational complexity. When applied to conforming finite element discretizations of elliptic problems and Maxwell equations, the method's convergence rates are very close to those for the nonadaptive version. Furthermore, the smoothers remain efficient for high order finite elements. We discuss the implementation in a general finite element code using the example of the deal.II library. |
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| Item Description: | Gesehen am 04.07.2022 Im Titel ist die Zahl 1 und der Ausdruck "curl" hochgestellt |
| Physical Description: | Online Resource |
| ISSN: | 1095-7197 |
| DOI: | 10.1137/090778523 |