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Finite volume schemes for fully non-linear elliptic equationsin divergence form

Published online by Cambridge University Press:  15 February 2007

Jérôme Droniou
Jérôme Droniou*
Affiliation:
Département de Mathématiques, UMR CNRS 5149, CC 051, Université Montpellier II, Place Eugène Bataillon, 34095 Montpellier cedex 5, France. droniou@math.univ-montp2.fr
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Abstract

We construct finite volume schemes, on unstructured and irregular grids andin any space dimension, for non-linear elliptic equations of the p-Laplacian kind: -div(|∇u|p-2 ∇u) = ƒ(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.

Keywords

Finite volume schemesirregular gridsnon-linear elliptic equationsLeray-Lions operators.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 40 , Issue 6 , November 2006 , pp. 1069 - 1100
Copyright
© EDP Sciences, SMAI, 2007

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