Gradient schemes: generic tools for the numerical analysis of diffusion equations

Jérôme Droniou (1) , Robert Eymard (2) , Raphaele Herbin (3)

1 School of Mathematical Sciences [Clayton]
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
3 LATP - Laboratoire d'Analyse, Topologie, Probabilités

The gradient scheme framework is based on a small number of properties and encompasses a large number of numerical methods. We recall these properties and develop some new generic tools associated with the gradient scheme framework. These tools enable us to prove that classical schemes are indeed gradient schemes, and allow us to perform a complete and generic study of the well-known (but rarely well-studied) mass lumping process.

Mots clés: gradient scheme; gradient discretisation; numerical scheme; diffusion equations; convergence analysis; discrete functional analysis

Domaines: Analyse numérique [math.NA]

Jérôme Droniou, Robert Eymard, Raphaele Herbin. Gradient schemes: generic tools for the numerical analysis of diffusion equations . 2015. ⟨hal-01150517v1⟩