Mathematics for Modeling and Scientific Computing by Goudon Thierry;

Author:Goudon, Thierry;
Language: eng
Format: epub
Publisher: John Wiley & Sons, Incorporated
Published: 2016-10-25T10:08:37+00:00

with k a matrix of MN(), such that 0 < K|ξ|2 ≤ k(x)ξ ≤ K|ξ|2 with k, K > 0, this approximation is not enough: it only provides an approximation of the gradient of u in the direction of the normal vector n(y), while we now need to know ∇u in the transverse direction to evaluate .

These questions are strongly motivated by applications related to the simulation of flows in porous media. For those applications, methods based on finite difference or finite element approximations have reached certain limits, especially for very heterogeneous environments. The subject is an area of active research, especially since the developments of [COU 99, DOM 05], which have provided clues to manage those difficulties in constructing an effective approximation of on control volume interfaces. The reference work [EYM 00] provides a more complete overview of these finite volume methods and their analysis.

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