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January & February  2009, 23(1&2): 265-280. doi: 10.3934/dcds.2009.23.265

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

Olivier Pironneau 1, , Alexei Lozinski 2, , Alain Perronnet 1, and  Frédéric Hecht 1,

1. 

LJLL, Université Pierre et Marie Curie, 175 rue du Chevaleret, 75013 Paris, France, France, France
2. 

Dept. Mathématiques,, Université Paul Sabbatier, 118, route de Narbonne, 31062 Toulouse, France

Received  December 2007 Revised  March 2008 Published  September 2008

We propose a technique for interactive mesh refinement in regions where the solution of a partial differential equation is less regular. 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.
Keywords: Finite Element, Chimera, Numerical Zoom, Multiscale, Porous Media Flow, Domain Decomposition.
Mathematics Subject Classification: Primary: 65N50, 65N15; Secondary: 65Y20.
Citation: Olivier Pironneau, Alexei Lozinski, Alain Perronnet, Frédéric Hecht. Numerical zoom for multiscale problems with an application to flows through porous media. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 265-280. doi: 10.3934/dcds.2009.23.265
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