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 |
|---|---|
| Pages (from-to) | 1069-1100 |
| Number of pages | 32 |
| Journal | Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique |
| 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
Cite this
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Finite volume schemes for fully non-linear elliptic equations in divergence form. / Droniou, Jerome.
In: Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique, Vol. 40, No. 6, 01.11.2006, p. 1069-1100.Research output: Contribution to journal › Article › Research › peer-review
TY - JOUR
T1 - Finite volume schemes for fully non-linear elliptic equations in divergence form
AU - Droniou, Jerome
PY - 2006/11/1
Y1 - 2006/11/1
N2 - 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.
AB - 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.
KW - Finite volume schemes
KW - Irregular grids
KW - Leray-Lions operators
KW - Non-linear elliptic equations
UR - http://www.scopus.com/inward/record.url?scp=33847227277&partnerID=8YFLogxK
U2 - 10.1051/m2an:2007001
DO - 10.1051/m2an:2007001
M3 - Article
VL - 40
SP - 1069
EP - 1100
JO - Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique
JF - Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique
SN - 0764-583X
IS - 6
ER -