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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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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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container_title	Applied numerical mathematics
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creator	Rodrigo, C. Gaspar, F.J. Lisbona, F.J.
description	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.
doi_str_mv	10.1016/j.apnum.2016.02.006
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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
title	On a local Fourier analysis for overlapping block smoothers on triangular grids
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