A 3D DISCRETE DUALITY FINITE VOLUME METHOD FOR NONLINEAR ELLIPTIC EQUATIONS

Yves Coudière (1) , Florence Hubert (2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités

Discrete Duality Finite Volume (DDFV) schemes have recently been developed in 2D to approximate nonlinear diffusion problems on general meshes. In this paper, a 3D extension of these schemes is proposed. The construction of this extension is detailed and its main properties are proved: a priori bounds, well-posedness and error estimates. The practical implementation of this scheme is easy. Numerical experiments are presented to illustrate its good behavior.

Mots clés: Finite-volume methods. Error estimates. Leray-Lions operators; Finite-volume methods. Error estimates. Leray-Lions operators.

Domaines: Analyse numérique [math.NA]

Yves Coudière, Florence Hubert. A 3D DISCRETE DUALITY FINITE VOLUME METHOD FOR NONLINEAR ELLIPTIC EQUATIONS. SIAM Journal on Scientific Computing, 2011, 33 (4), pp.1739--1764. ⟨10.1137/100786046⟩. ⟨hal-00456837⟩