Analysis of the second phase of the GMRES convergence for a convection-diffusion model problem

Please always quote using this URN:urn:nbn:de:0296-matheon-9822
  • It is well konwn that GMRES applied to linear algebraic systems arising from a convection-diffusion model problem that has been discretized by the streamline upwind Petrov-Galerkin (SUPG) method, typically displays two distinct phases of convergence: a slow initial phase followed by a convergence acceleration in the second phase. This paper complements the known results on the length of the initial phase by analyzing how the acceleration in the second phase of convergence is related to the mesh Peclet number and the choice of the stabilization parameter in the SUPG discretization. The analysis is based on some new expressions and bounds for the GMRES residuals, which can be of general interest.

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Author:Jurjen Duintjer-Tebbens, Jörg Liesen, Zdenĕk Strakoš
Referee:Carsten Carstensen
Document Type:Preprint, Research Center Matheon
Date of first Publication:2012/01/18
Release Date:2012/01/18
Tag:GMRES; SDFEM discretization; SUPG discretization; convection-diffusion problem; convergence bounds
Institute:Technische Universität Berlin
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F10 Iterative methods for linear systems [See also 65N22]
65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F15 Eigenvalues, eigenvectors
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N22 Solution of discretized equations [See also 65Fxx, 65Hxx]
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Preprint Number:861
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