Preconditioner for a Laplace grid operator on a condensed grid
A.M. Matsokin
Keywords: Dirichlet boundary value problem for the Poisson equation, finite element method with piecewise-linear functions, condensed grid (topologically equivalent to a rectangular grid), preconditioner
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.
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