Numerical zoom for multiscale problems with an application to flows through porous media

Olivier Pironneau; Alexei Lozinski; Alain Perronnet; Frédéric Hecht

doi:10.3934/dcds.2009.23.265

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2009, Volume 23, Issue 1&2: 265-280. Doi: 10.3934/dcds.2009.23.265

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Numerical zoom for multiscale problems with an application to flows through porous media

1.
LJLL, Université Pierre et Marie Curie, 175 rue du Chevaleret, 75013 Paris
2.
Dept. Mathématiques,, Université Paul Sabbatier, 118, route de Narbonne, 31062 Toulouse

Received: November 30, 2007

Revised: February 29, 2008

Published: April 2009

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Abstract

We propose a technique for interactive mesh refinement in regionswhere the solution of a partial differential equation is lessregular. Based on the method of harmonic patches, the idea is to bypass an expensive calculation on a fine mesh and yet retain the same accuracy with several much smaller computations. A general numerical zoom method is presented; then it is specialized to the case where the mesh in the zoom is a refinement of the coarse mesh; it is also compared with classic domain decomposition algorithms. Numerical examples are given for a porous flow modeled by Darcy's law.

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Mathematics Subject Classification: Primary: 65N50, 65N15; Secondary: 65Y20.

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