The Australian Journal of Mathematical Analysis and Applications

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ISSN 1449-5910  


Paper Information

Paper Title:

Finite Volume Approximation of a Class of 2D Elliptic Equations with Discontinuous and Highly Oscillating Coefficients


J. D. Bambi Pemba and B. Ondami

Université Marien Ngouabi
Factuté des Sciences et Techniques
BP 69 Brazzaville,


In this paper, we are interested in the Finite Volume approximation of a second-order two-dimensional elliptic equation in heterogeneous porous medium with a periodic structure. The equation's coefficients are therefore discontinuous and highly oscillating. This class of problems has been extensively studied in the literature, where various methods proposed for determining the so-called homogenized problem. What we are particularly interested in is the direct numerical approximation of the problem, which has received little attention in the literature. We use the cell-centered finite volume approach for this purpose. Error estimates are established, and numerical simulations are conducted for both the isotropic and anisotropic media cases. The obtained solution is compared to the homogenized solution, and the results show that this approach provides an adequate approximation of the exact solution.

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