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

Droniou, Jérôme

doi:10.1051/m2an:2007001

Droniou, Jérôme

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

Résumé

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: $- div (| \nabla u |^{p - 2} \nabla u) = f$ (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.

MR Zbl

DOI : 10.1051/m2an:2007001

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

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     author = {Droniou, J\'er\^ome},
     title = {Finite volume schemes for fully non-linear elliptic equations in divergence form},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     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 = {https://www.numdam.org/articles/10.1051/m2an:2007001/}
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Droniou, Jérôme. Finite volume schemes for fully non-linear elliptic equations in divergence form. ESAIM: Modélisation mathématique et analyse numérique, Tome 40 (2006) no. 6, pp. 1069-1100. doi : 10.1051/m2an:2007001. https://www.numdam.org/articles/10.1051/m2an:2007001/

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