This book introduces the basic ideas to build discontinuous Galerkin methods and, at the
same time, incorporates several recent mathematical developments. The presentation is to a …

This work concerns linearization methods for efficiently solving the Richards equation, a
degenerate elliptic-parabolic equation which models flow in saturated/unsaturated porous …

Abstract The Hermitian and skew-Hermitian splitting iteration method (HSS) is commonly an
effective linear iterative method for solving sparse non-Hermite positive definite equations …

We establish residual a posteriori error estimates for lowest-order Raviart–Thomas mixed
finite element discretizations of convection-diffusion-reaction equations on simplicial …

We propose a second order finite volume scheme for nonlinear degenerate parabolic
equations which admit an entropy functional. For some of these models (porous media …

Finite-volume methods for problems involving second-order operators with full diffusion
matrix can be used thanks to the definition of a discrete gradient for piecewise constant …

In this work, we consider the transport of a surfactant in variably saturated porous media.
The water flow is modelled by the Richards equations and it is fully coupled with the …

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

We propose a finite volume scheme for convection–diffusion equations with nonlinear
diffusion. Such equations arise in numerous physical contexts. We will particularly focus on …

We consider a numerical scheme for a class of degenerate parabolic equations, including
both slow and fast diffusion cases. A particular example in this sense is the Richards …