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

Abstract

Abstract 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 H 1 ‐, L 2 ‐ and L ∞ ‐norm for small data and convergence in H 1 ‐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.