We present a numerical method for approximating the solutions of degenerate parabolic
equations with a formal gradient flow structure. The numerical method we propose …

The nonlinear systems obtained by discretizing degenerate parabolic equations may be
hard to solve, especially with Newton's method. In this paper, we apply to the Richards …

In this paper we consider a unipolar degenerate drift-diffusion system where the relation
between the concentration of the charged species and the chemical potential is. We design …

We propose a variational finite volume scheme to approximate the solutions to Wasserstein
gradient flows. The time discretization is based on an implicit linearization of the …

Gradient schemes is a framework that enables the unified convergence analysis of many
numerical methods for elliptic and parabolic partial differential equations: conforming and …

We propose a nonlinear Discrete Duality Finite Volume scheme to approximate the solutions
of drift diffusion equations. The scheme is built to preserve at the discrete level even on …

This paper deals with the existence of global weak solutions for a wide class of (multiple
species) cross-diffusions systems. The existence is based on two different ingredients: an …

We consider a degenerate parabolic system modeling the flow of fresh and saltwater in a
porous medium in the context of seawater intrusion. We propose and analyze a finite volume …

We study a finite volume scheme for the approximation of the solution to convection diffusion
equations with nonlinear convection and Robin boundary conditions. The scheme builds on …

We describe the competitive motion of N+ 1 incompressible immiscible phases within a
porous medium as the gradient flow of a singular energy in the space of nonnegative …