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.
|Number of pages||32|
|Journal||Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique|
|Publication status||Published - 1 Nov 2006|
- Finite volume schemes
- Irregular grids
- Leray-Lions operators
- Non-linear elliptic equations