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Criteria for the approximation property for multigrid methods in nonnested spaces


Authors: Nicolas Neuss and Christian Wieners
Journal: Math. Comp. 73 (2004), 1583-1600
MSC (2000): Primary 65N55, 65F10
DOI: https://doi.org/10.1090/S0025-5718-04-01628-X
Published electronically: March 9, 2004
MathSciNet review: 2059727
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Abstract: We extend the abstract frameworks for the multigrid analysis for nonconforming finite elements to the case where the assumptions of the second Strang lemma are violated. The consistency error is studied in detail for finite element discretizations on domains with curved boundaries. This is applied to prove the approximation property for conforming elements, stabilized $Q_1/P_0$-elements, and nonconforming elements for linear elasticity on nonpolygonal domains.


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Additional Information

Nicolas Neuss
Affiliation: Universität Heidelberg, IWR, Im Neuenheimer Feld 368, 69120 Heidelberg, Germany
Email: nicolas.neuss@iwr.uni-heidelberg.de

Christian Wieners
Affiliation: Universität Karlsruhe (TH), Institut für Praktische Mathematik, Engesser Str. 2, 76128 Karlsruhe, Germany
Email: wieners@math.uni-karlsruhe.de

DOI: https://doi.org/10.1090/S0025-5718-04-01628-X
Keywords: Multigrid analysis, nonnested forms, approximation property, curved boundaries, stabilized finite elements
Received by editor(s): January 23, 2001
Received by editor(s) in revised form: March 21, 2003
Published electronically: March 9, 2004
Additional Notes: This work was supported in part by the Deutsche Forschungsgemeinschaft
Article copyright: © Copyright 2004 American Mathematical Society

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