A finite volume element method for a non-linear elliptic problem

We consider a finite volume discretization of second‐order non‐linear elliptic boundary value problems on polygonal domains. Using relatively standard assumptions we show the existence of the finite volume solution. Furthermore, for a sufficiently small data the uniqueness of the finite volume solut...

Full description

Saved in:
Bibliographic Details
Published in:Numerical linear algebra with applications 2005-06, Vol.12 (5-6), p.515-546
Main Authors: Chatzipantelidis, P., Ginting, V., Lazarov, R. D.
Format: Article
Language:English
Subjects:
error estimates
finite volume element method
fixed point iterations
Newton's method
non-linear elliptic equation
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We consider a finite volume discretization of second‐order non‐linear elliptic boundary value problems on polygonal domains. Using relatively standard assumptions we show the existence of the finite volume solution. Furthermore, for a sufficiently small data the uniqueness of the finite volume solution may also be deduced. We derive error estimates in H1‐, L2‐ and L∞‐norm for small data and convergence in H1‐norm for large data. In addition a Newton's method is analysed for the approximation of the finite volume solution and numerical experiments are presented. Copyright © 2005 John Wiley & Sons, Ltd.
ISSN:1070-5325
1099-1506
DOI:10.1002/nla.439