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: -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.
Original language | English |
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Pages (from-to) | 1069-1100 |
Number of pages | 32 |
Journal | ESAIM: Mathematical Modelling and Numerical Analysis |
Volume | 40 |
Issue number | 6 |
DOIs | |
Publication status | Published - 1 Nov 2006 |
Externally published | Yes |
Keywords
- Finite volume schemes
- Irregular grids
- Leray-Lions operators
- Non-linear elliptic equations