# Finite volume schemes for fully non-linear elliptic equations in divergence form

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

- Volume: 40, Issue: 6, page 1069-1100
- ISSN: 0764-583X

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topDroniou, Jérôme. "Finite volume schemes for fully non-linear elliptic equations in divergence form." ESAIM: Mathematical Modelling and Numerical Analysis 40.6 (2007): 1069-1100. <http://eudml.org/doc/194345>.

@article{Droniou2007,

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) = 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.
},

author = {Droniou, Jérôme},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Finite volume schemes; irregular grids; non-linear elliptic equations;
Leray-Lions operators.; finite volume schemes; nonlinear elliptic equations; Leray-Lions operators; numerical results},

language = {eng},

month = {2},

number = {6},

pages = {1069-1100},

publisher = {EDP Sciences},

title = {Finite volume schemes for fully non-linear elliptic equations in divergence form},

url = {http://eudml.org/doc/194345},

volume = {40},

year = {2007},

}

TY - JOUR

AU - Droniou, Jérôme

TI - Finite volume schemes for fully non-linear elliptic equations in divergence form

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2007/2//

PB - EDP Sciences

VL - 40

IS - 6

SP - 1069

EP - 1100

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) = 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.

LA - eng

KW - Finite volume schemes; irregular grids; non-linear elliptic equations;
Leray-Lions operators.; finite volume schemes; nonlinear elliptic equations; Leray-Lions operators; numerical results

UR - http://eudml.org/doc/194345

ER -

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