In this paper, we are interested in the numerical approximation of a class of two-dimensional parabolic equations having discontinuous, periodic, and highly oscillating coefficients. We use the method of lines with a finite volume approach to discretize this equation. This discretization leads to an ordinary differential equation (ODE) that we discretize by the Euler implicit scheme. Numerical experiments comparing the obtained solution and the so-called homogenized solution show that the method accuracy depends on the homogenization parameter.

porous media, homogenization, parabolic equation, finite volume method, method of lines, ordinary differential equation (ODE), implicit numerical scheme.

Received: September 28, 2022; Revised: November 9, 2022; Accepted: November 19, 2022; Published: January 7, 2023

How to cite this article: Drainne Jualix Bambi Pemba and Bienvenu Ondami, Finite volume approximation of a class of two-dimensional parabolic equations with discontinuous and highly oscillating coefficients, International Journal of Numerical Methods and Applications 23(1) (2023), 51-65. http://dx.doi.org/10.17654/0975045223003

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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