Convergence of nonlinear finite volume schemes for heterogeneous anisotropic diffusion on general meshes

Martin Schneider (1) , Léo Agélas (2) , Guillaume Enchéry (2) , Bernd Flemisch (1)

1 University of Stuttgart
2 IFPEN - IFP Energies nouvelles

In the present work, we deal with the convergence of cell-centered nonlinear finite volume schemes for anisotropic and heterogeneous diffusion operators. A general framework for the convergence study of finite volume methods is provided and used to establish the convergence of the new methods. Thorough assessment on a set of anisotropic heterogeneous problems as well as a comparison with linear finite volume schemes is provided.

Mots clés: multi-point flux approximation; finite volume methods; heterogeneous anisotropic diffusion; monotone; convergence analysis

Domaines: Analyse numérique [math.NA]

Martin Schneider, Léo Agélas, Guillaume Enchéry, Bernd Flemisch. Convergence of nonlinear finite volume schemes for heterogeneous anisotropic diffusion on general meshes. Journal of Computational Physics, 2017, 351, pp.80-107. ⟨10.1016/j.jcp.2017.09.003⟩. ⟨hal-01758157⟩