Author(s)

Hubert Donfack

Department of Mathematics and Computer Sciences, The Bamenda University, Bamenda, Cameroon.

This paper presents and analyzes a Discrete Duality Finite Volume (DDFV) method to solve 2D diffusion problems under prescribed Robin boundary conditions. The derivation of a symmetric discrete problem is established. The existence and uniqueness of a solution to this discrete problem are shown via the positive definiteness of its associated matrix. We show that the discrete scheme meets the Neumann problem when the parameter $\alpha \to 0$ (and, in a sense, when $\alpha \to \infty$ the Dirichlet problem). This work is a continuation of our work regarding the development of DDFV methods. The main innovation here is taking into account Robin’s boundary conditions. We provide a few steps of Matlab implementation and numerical tests to confirm the effectiveness of the method.

Finite Volume Schemes, Discontinuous Coefficients, Diffusion Problems, Homogeneous Porous Media

Donfack, H. (2025) Discrete Duality Finite Volume for Anisotropic Diffusion Problems with Prescribed Robin Boundary Conditions. Journal of Applied Mathematics and Physics, 13, 4016-4045. doi: 10.4236/jamp.2025.1311225.