On the invertibility of mappings arising in 2D grid generation problems

Ph. Clement, Rob Hagmeijer, G. Sweers

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Abstract

In adapting a grid for a Computational Fluid Dynamics problem one uses a mapping from the unit square onto itself that is the solution of an elliptic partial differential equation with rapidly varying coefficients. For a regular discretization this mapping has to be invertible. We will show that such result holds for general elliptic operators (in two dimensions). The Carleman-Hartman-Wintner Theorem will be fundamental in our proof. We will also explain why such a general result cannot be expected to hold for the (three-dimensional) cube.
Original languageUndefined
Pages (from-to)37-52
JournalNumerische Mathematik
Volume73
Issue number1
DOIs
Publication statusPublished - Mar 1996

Keywords

  • IR-58056

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