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Asymptotic and numerical modelling of flows in fractured porous media

Philippe AngotFranck BoyerFlorence Hubert — 2009

ESAIM: Mathematical Modelling and Numerical Analysis

This study concerns some asymptotic models used to compute the flow outside and inside fractures in a bidimensional porous medium. The flow is governed by the Darcy law both in the fractures and in the porous matrix with large discontinuities in the permeability tensor. These fractures are supposed to have a small thickness with respect to the macroscopic length scale, so that we can asymptotically reduce them to immersed polygonal fault interfaces and the model finally consists in a coupling between...

Analysis of a combined barycentric finite volume—nonconforming finite element method for nonlinear convection-diffusion problems

Philippe AngotVít DolejšíMiloslav FeistauerJiří Felcman — 1998

Applications of Mathematics

We present the convergence analysis of an efficient numerical method for the solution of an initial-boundary value problem for a scalar nonlinear conservation law equation with a diffusion term. Nonlinear convective terms are approximated with the aid of a monotone finite volume scheme considered over the finite volume barycentric mesh, whereas the diffusion term is discretized by piecewise linear nonconforming triangular finite elements. Under the assumption that the triangulations are of weakly...

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