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non-linear elliptic equations

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Finite volume schemes for fully non-linear elliptic equationsin divergence form
Jérôme Droniou
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 40 / Issue 6 / November 2006

Published online by Cambridge University Press:

15 February 2007, pp. 1069-1100

Print publication:

November 2006
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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.