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Boyer, F. and Hubert, F. (2008) Finite Volume Method for 2D Linear and Nonlinear Elliptic Problems with Discontinuities. SIAM Journal on Numerical Analysis, 46, 3032-3070.
https://doi.org/10.1137/060666196

has been cited by the following article:

• TITLE: Discrete Duality Finite Volume for Anisotropic Diffusion Problems with Prescribed Robin Boundary Conditions

  AUTHORS: Hubert Donfack

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

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.13 No.11, November 21, 2025

  ABSTRACT: 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 α→0 (and, in a sense, when α→∞ 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.