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We construct finite volume schemes, on unstructured and irregular grids and in any space dimension, for non-linear elliptic equations of the -laplacian kind: (with ). 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.
@article{M2AN_2006__40_6_1069_0,
author = {Droniou, J\'er\^ome},
title = {Finite volume schemes for fully non-linear elliptic equations in divergence form},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1069--1100},
publisher = {EDP-Sciences},
volume = {40},
number = {6},
year = {2006},
doi = {10.1051/m2an:2007001},
mrnumber = {2297105},
zbl = {1117.65154},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2007001/}
}
TY - JOUR AU - Droniou, Jérôme TI - Finite volume schemes for fully non-linear elliptic equations in divergence form JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2006 SP - 1069 EP - 1100 VL - 40 IS - 6 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an:2007001/ DO - 10.1051/m2an:2007001 LA - en ID - M2AN_2006__40_6_1069_0 ER -
%0 Journal Article %A Droniou, Jérôme %T Finite volume schemes for fully non-linear elliptic equations in divergence form %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2006 %P 1069-1100 %V 40 %N 6 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an:2007001/ %R 10.1051/m2an:2007001 %G en %F M2AN_2006__40_6_1069_0
Droniou, Jérôme. Finite volume schemes for fully non-linear elliptic equations in divergence form. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 40 (2006) no. 6, pp. 1069-1100. doi: 10.1051/m2an:2007001
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