Dedicated to Owe Axelsson on the occasion of his 70th birthday.
A finite volume element method for a non-linear elliptic problem†
Article first published online: 3 MAY 2005
Copyright © 2005 John Wiley & Sons, Ltd.
Numerical Linear Algebra with Applications
Special Issue: On the occasion of the 70th birthday of Owe Axelsson
Volume 12, Issue 5-6, pages 515–546, June - August 2005
How to Cite
Chatzipantelidis, P., Ginting, V. and Lazarov, R. D. (2005), A finite volume element method for a non-linear elliptic problem. Numer. Linear Algebra Appl., 12: 515–546. doi: 10.1002/nla.439
- Issue published online: 14 JUN 2005
- Article first published online: 3 MAY 2005
- Manuscript Revised: 30 OCT 2004
- Manuscript Received: 26 MAR 2004
- finite volume element method;
- non-linear elliptic equation;
- error estimates;
- fixed point iterations;
- Newton's method
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.