


Paper's Title:
Finite Volume Approximation of a Class of 2D Elliptic Equations with Discontinuous and Highly Oscillating Coefficients
Author(s):
J. D. Bambi Pemba and B. Ondami
Université Marien Ngouabi
Factuté des Sciences et Techniques
BP 69 Brazzaville,
Congo.
Email: bondami@gmail.com
URL:
https://www.researchgate.net/profile/BienvenuOndami
https://www.linkedin.com/in/bienvenuondami
Abstract:
In this paper, we are interested in the Finite Volume approximation of a secondorder twodimensional 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 socalled 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 cellcentered 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.
Paper's Title:
The RAFU remainder in Taylor's formula
Author(s):
A. C. Sanchez
''Santa Eulalia'' High School,
Spain
Email: csanchezalicia@gmail.com
Abstract:
This work is about the remainder in Taylor's formula. Specifically, the RAFU remainder is studied. Its mathematical expression is given. Some examples are shown. Different ways to obtain this remainder are developed.
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