Sibirskii Zhurnal Vychislitel'noi Matematiki
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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2013, Volume 16, Number 2, Pages 165–170 (Mi sjvm507)  
Preconditioner for a Laplace grid operator on a condensed grid

A. M. Matsokinab

a Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University, Novosibirsk
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Abstract: In this paper, it is proved that a Laplace grid operator approximating a Dirichlet boundary value problem for the Poisson equation by the finite element method with piecewise-linear functions on an evenly condensed grid that is topologically equivalent to a rectangular grid (i.e. obtained by shifting the rectangular grid nodes) is equivalent, in the range, to the operator of a $5$-point difference scheme on a uniform grid.
Key words: Dirichlet boundary value problem for the Poisson equation, finite element method with piecewise-linear functions, condensed grid (topologically equivalent to a rectangular grid), preconditioner.
Received: 04.05.2012
Revised: 11.09.2012
English version:
Numerical Analysis and Applications, 2013, Volume 6, Issue 2, Pages 145–150
DOI: https://doi.org/10.1134/S1995423913020067
Bibliographic databases:
Document Type: Article
UDC: 518.12
Language: Russian
Citation: A. M. Matsokin, “Preconditioner for a Laplace grid operator on a condensed grid”, Sib. Zh. Vychisl. Mat., 16:2 (2013), 165–170; Num. Anal. Appl., 6:2 (2013), 145–150
Citation in format AMSBIB
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\paper Preconditioner for a~Laplace grid operator on a~condensed grid
\jour Sib. Zh. Vychisl. Mat.
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\vol 16
\issue 2
\pages 165--170
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\transl
\jour Num. Anal. Appl.
\yr 2013
\vol 6
\issue 2
\pages 145--150
\crossref{https://doi.org/10.1134/S1995423913020067}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84878845311}
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