This paper is concerned with the finite volume approximation of the p-laplacian equation with homogeneous Dirichlet boundary conditions on rectangular meshes. A reconstruction of the norm of the gradient on the mesh’s interfaces is needed in order to discretize the p-laplacian operator. We give a detailed description of the possible nine points schemes ensuring that the solution of the resulting finite dimensional nonlinear system exists and is unique. These schemes, called admissible, are locally conservative and in addition derive from the minimization of a strictly convexe and coercive discrete functional. The convergence rate is analyzed when the solution lies in . Numerical results are given in order to compare different admissible and non-admissible schemes.
Mots-clés : finite volume methods, p-laplacian, error estimates
@article{M2AN_2004__38_6_931_0,
author = {Andreianov, Boris and Boyer, Franck and Hubert, Florence},
title = {Finite volume schemes for the $p$-laplacian on cartesian meshes},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {931--959},
publisher = {EDP-Sciences},
volume = {38},
number = {6},
year = {2004},
doi = {10.1051/m2an:2004045},
mrnumber = {2108939},
zbl = {1081.65105},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an:2004045/}
}
TY - JOUR AU - Andreianov, Boris AU - Boyer, Franck AU - Hubert, Florence TI - Finite volume schemes for the $p$-laplacian on cartesian meshes JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2004 SP - 931 EP - 959 VL - 38 IS - 6 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an:2004045/ DO - 10.1051/m2an:2004045 LA - en ID - M2AN_2004__38_6_931_0 ER -
%0 Journal Article %A Andreianov, Boris %A Boyer, Franck %A Hubert, Florence %T Finite volume schemes for the $p$-laplacian on cartesian meshes %J ESAIM: Modélisation mathématique et analyse numérique %D 2004 %P 931-959 %V 38 %N 6 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an:2004045/ %R 10.1051/m2an:2004045 %G en %F M2AN_2004__38_6_931_0
Andreianov, Boris; Boyer, Franck; Hubert, Florence. Finite volume schemes for the $p$-laplacian on cartesian meshes. ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 6, pp. 931-959. doi : 10.1051/m2an:2004045. http://archive.numdam.org/articles/10.1051/m2an:2004045/
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