We present Finite Volume methods for diffusion equations on generic meshes, that received
important coverage in the last decade or so. After introducing the main ideas and …

We present two new cell-centered nonlinear finite-volume methods for the heterogeneous,
anisotropic diffusion problem. The schemes split the interfacial flux into harmonic and …

We present a new second-order accurate monotone finite volume (FV) method for the steady-
state advection–diffusion equation. The method uses a nonlinear approximation for both …

We propose a cell-centered finite volume (FV) scheme with the minimal stencil formed by the
closest neighbouring cells. The discrete solution satisfies the discrete maximum principle …

We present a new nonlinear monotone finite volume method for diffusion equation and its
application to two-phase flow model. We consider full anisotropic discontinuous diffusion or …

In this paper, a nonlinear positivity-preserving finite volume scheme for the heterogeneous
and anisotropic diffusion problems is proposed. Firstly, a linear diamond finite volume …

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 …

This article presents a new positivity-preserving finite-volume scheme with a nonlinear two-
point flux approximation, which uses optimization techniques for the face stencil calculation …

We present in this article a positive finite volume method for diffusion equation on deformed
meshes. This method is mainly inspired from, and uses auxiliary unknowns at the nodes of …

We consider the solution of systems of nonlinear algebraic equations that appear in a
positivity preserving finite volume scheme for steady-state advection-diffusion equations. We …