On a local Fourier analysis for overlapping block smoothers on triangular grids

A general local Fourier analysis for overlapping block smoothers on triangular grids is presented. This analysis is explained in a general form for its application to problems with different discretizations. This tool is demonstrated for two different problems: a stabilized linear finite element dis...

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Bibliographic Details
Published in:Applied numerical mathematics 2016-07, Vol.105, p.96-111
Main Authors: Rodrigo, C., Gaspar, F.J., Lisbona, F.J.
Format: Article
Language:English
Subjects:
Asymptotic properties
Blocking
Box-relaxation
Convergence
Discretization
Finite element method
Fourier analysis
Local Fourier analysis
Mathematical analysis
Mathematical models
Multigrid
Nédélec
Overlapping block smoothers
Saddle point type problems
Stokes
Triangular grids
Vanka smoothers
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Summary:A general local Fourier analysis for overlapping block smoothers on triangular grids is presented. This analysis is explained in a general form for its application to problems with different discretizations. This tool is demonstrated for two different problems: a stabilized linear finite element discretization of Stokes equations and an edge-based discretization of the curl–curl operator by lowest-order Nédélec finite element method. In this latter, special Fourier modes have to be considered in order to perform the analysis. Numerical results comparing two- and three-grid convergence factors predicted by the local Fourier analysis to real asymptotic convergence factors are presented to confirm the predictions of the analysis and show their usefulness.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2016.02.006