Preconditioner for a Laplace grid operator on a condensed grid

A. M. Matsokin<sup>ab

a</sup> Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Novosibirsk State University, Novosibirsk

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.

UDC: 518.12

Received: 04.05.2012
Revised: 11.09.2012

 English version: Numerical Analysis and Applications, 2013, 6:2, 145–150

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