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

Jérôme Droniou

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2006)

  • Volume: 40, Issue: 6, page 1069-1100
  • ISSN: 0764-583X

Abstract

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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 p -laplacian kind: - div ( | ∇ u | p - 2 ∇ u ) = f (with 1 < p < ∞ ). 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.

How to cite

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Droniou, Jérôme. "Finite volume schemes for fully non-linear elliptic equations in divergence form." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 40.6 (2006): 1069-1100. <http://eudml.org/doc/245591>.

@article{Droniou2006,
abstract = {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: $-\operatorname\{div\}(|\nabla u|^\{p-2\}\nabla u)=f$ (with $1&lt;p&lt;\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.},
author = {Droniou, Jérôme},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {finite volume schemes; irregular grids; non-linear elliptic equations; Leray-Lions operators; nonlinear elliptic equations; numerical results},
language = {eng},
number = {6},
pages = {1069-1100},
publisher = {EDP-Sciences},
title = {Finite volume schemes for fully non-linear elliptic equations in divergence form},
url = {http://eudml.org/doc/245591},
volume = {40},
year = {2006},
}

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 - Modélisation Mathématique et Analyse Numérique
PY - 2006
PB - EDP-Sciences
VL - 40
IS - 6
SP - 1069
EP - 1100
AB - 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: $-\operatorname{div}(|\nabla u|^{p-2}\nabla u)=f$ (with $1&lt;p&lt;\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.
LA - eng
KW - finite volume schemes; irregular grids; non-linear elliptic equations; Leray-Lions operators; nonlinear elliptic equations; numerical results
UR - http://eudml.org/doc/245591
ER -

References

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