Uniform convergence of multigrid V-cycle on adaptively refined finite element meshes for second order elliptic problems

In this paper we prove the uniform convergence of the standard multigrid V-cycle algorithm with the Gauss-Seidel relaxation performed only on the new nodes and their 'immediate' neighbors for discrete elliptic problems on the adaptively refined finite element meshes using the newest vertex...

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Veröffentlicht in:Science in China. Series A, Mathematics, physics, astronomy Jg. 49; H. 10; S. 1405 - 1429
Hauptverfasser: Wu, Haijun, Chen, Zhiming
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Department of Mathematics, Nanjing University, Nanjing 210093, China%Institute of Computational Mathematics, Chinese Academy of Sciences, Beijing 100080, China 01.10.2006
Schlagworte:
Scott-Zhang interpolation
adaptive finite element meshes
local relaxation
Multigrid V-cycle algorithm
ISSN:1006-9283, 1862-2763
Online-Zugang:Volltext
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Zusammenfassung:In this paper we prove the uniform convergence of the standard multigrid V-cycle algorithm with the Gauss-Seidel relaxation performed only on the new nodes and their 'immediate' neighbors for discrete elliptic problems on the adaptively refined finite element meshes using the newest vertex bisection algorithm. The proof depends on sharp estimates on the relationship of local mesh sizes and a new stability estimate for the space decomposition based on the Scott-Zhang interpolation operator. Extensive numerical results are reported, which confirm the theoretical analysis.
Bibliographie:ObjectType-Article-2
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ISSN:1006-9283
1862-2763
DOI:10.1007/s11425-006-2005-5