Hermeline, F. (2007) A Finite Volume Method for Approximating 3D Diffusion Operators on General Meshes. Computer Methods in Applied Mechanics and Engineering, 196, 2497-2526.
https://doi.org/10.1016/j.cma.2007.01.005

has been cited by the following article:

• TITLE: Numerical Solution of 2-D Diffusion Problems Using Discrete Duality Finite Volume Method on General Boundary Conditions

  AUTHORS: Hubert Donfack, Aubin Kinfack Jeutsa

  KEYWORDS: Flow Problems, Nonhomogeneous Anisotropic Media, Finite Volumes, Test Simulations

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.10 No.6, June 28, 2022

  ABSTRACT: In this paper, we present a discrete duality finite volume (DDFV) method for 2-D flow problems in nonhomogeneous anisotropic porous media under diverse boundary conditions. We use the discrete gradient defined in diamond cells to compute the fluxes. We focus on the case of Dirichlet, full Neumann and periodic boundary conditions. Taking into account the periodicity is the main new ingredient with respect to our recent works. We explain the procedures step by step, for numerical solutions. We develop a matlab code for algebraic equations. Numerical tests were provided to confirm our theoretical results.