Uniform convergence of Galerkin‐multigrid methods for nonconforming finite elements for second‐order problems with less than full elliptic regularity

Medientyp: E-Artikel
Titel: Uniform convergence of Galerkin‐multigrid methods for nonconforming finite elements for second‐order problems with less than full elliptic regularity
Beteiligte: Chen, Zhangxin
Erschienen: Wiley, 2002
Erschienen in: Numerical Methods for Partial Differential Equations, 18 (2002) 2, Seite 203-217
Sprache: Englisch
DOI: 10.1002/num.10004
ISSN: 0749-159X; 1098-2426
Schlagwörter: Applied Mathematics ; Computational Mathematics ; Numerical Analysis ; Analysis
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Beschreibung: AbstractIn this article we prove uniform convergence estimates for the recently developed Galerkin‐multigrid methods for nonconforming finite elements for second‐order problems with less than full elliptic regularity. These multigrid methods are defined in terms of the “Galerkin approach,” where quadratic forms over coarse grids are constructed using the quadratic form on the finest grid and iterated coarse‐to‐fine intergrid transfer operators. Previously, uniform estimates were obtained for problems with full elliptic regularity, whereas these estimates are derived with less than full elliptic regularity here. Applications to the nonconforming P1, rotated Q1, and Wilson finite elements are analyzed. The result applies to the mixed method based on finite elements that are equivalent to these nonconforming elements. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 203–217, 2002; DOI 10.1002/num.10004

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