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

Abstract 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.