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...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
2011
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| In: |
SIAM journal on scientific computing
Year: 2011, Jahrgang: 33, Heft: 4, Pages: 2095-2114 |
| ISSN: | 1095-7197 |
| DOI: | 10.1137/090778523 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1137/090778523 Verlag, lizenzpflichtig, Volltext: https://epubs.siam.org/doi/10.1137/090778523 
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| Verfasserangaben: | Bärbel Janssen and Guido Kanschat |
MARC
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| 245 | 1 | 0 | |a Adaptive multilevel methods with local smoothing for H1- and Hcurl-conforming high order finite element methods |c Bärbel Janssen and Guido Kanschat |
| 246 | 3 | 3 | |a Adaptive multilevel methods with local smoothing for H 1- and H curl-conforming high order finite element methods |
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| 520 | |a 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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| 650 | 4 | |a finite element method | |
| 650 | 4 | |a hanging nodes | |
| 650 | 4 | |a Maxwell equations | |
| 650 | 4 | |a multigrid methods | |
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