Finite volume schemes for fully non-linear elliptic equations in divergence form

Jerome Droniou (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

We construct finite volume schemes, on unstructured and irregular grids, for non-linear elliptic equations of the p-Laplacian kind: -div(|Du|^{p-2}Du)=f. We prove the existence and uniqueness of the approximate solutions, as well as their strong convergence towards the solution of the PDE. The outcome of some numerical tests are also provided.

Mots clés: finite volume schemes; irregular grids; non-linear elliptic equations; Leray-Lions operators

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Jerome Droniou. Finite volume schemes for fully non-linear elliptic equations in divergence form. 2006. ⟨hal-00009614v3⟩