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

Droniou, Jérôme

ESAIM: Modélisation mathématique et analyse numérique, Tome 40 (2006) no. 6, pp. 1069-1100.

We construct finite volume schemes, on unstructured and irregular grids and in any space dimension, for non-linear elliptic equations of the $p$-laplacian kind: $-div\left(\right|\nabla u{|}^{p-2}\nabla u)=f$ (with $1<p<\infty$). 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.

Classification : 65N12, 35J65, 65N30
Mots clés : finite volume schemes, irregular grids, non-linear elliptic equations, Leray-Lions operators

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