Criteria for the approximation property for multigrid methods in nonnested spaces
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- by Nicolas Neuss and Christian Wieners PDF
- Math. Comp. 73 (2004), 1583-1600 Request permission
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.References
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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
- 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
- © Copyright 2004 American Mathematical Society
- Journal: Math. Comp. 73 (2004), 1583-1600
- MSC (2000): Primary 65N55, 65F10
- DOI: https://doi.org/10.1090/S0025-5718-04-01628-X
- MathSciNet review: 2059727