Volume 40, Number 6, November-December 2006
|Page(s)||1069 - 1100|
|Published online||15 February 2007|
Finite volume schemes for fully non-linear elliptic equations in divergence form
Département de Mathématiques, UMR CNRS 5149, CC 051, Université Montpellier II,
Place Eugène Bataillon, 34095 Montpellier cedex 5, France. email@example.com
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) = 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.
Mathematics Subject Classification: 65N12 / 35J65 / 65N30
Key words: Finite volume schemes / irregular grids / non-linear elliptic equations / Leray-Lions operators.
© EDP Sciences, SMAI, 2007
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