American Institute of Mathematical Sciences

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

 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 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.
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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