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non conforming meshes

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Small-stencil 3D schemes for diffusive flows in porous media
Robert Eymard, Cindy Guichard, Raphaèle Herbin
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 46 / Issue 2 / March 2012

Published online by Cambridge University Press:

12 October 2011, pp. 265-290

Print publication:

March 2012
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In this paper, we study some discretization schemes for diffusive flows in heterogeneous anisotropic porous media. We first introduce the notion of gradient scheme, and show that several existing schemes fall into this framework. Then, we construct two new gradient schemes which have the advantage of a small stencil. Numerical results obtained for real reservoir meshes show the efficiency of the new schemes, compared to existing ones.