Differential Equations and Nonlinear Mechanics
Volume 2006 (2006), Article ID 31797, 16 pages

Nonlinear elliptic problems with the method of finite volumes

Sanjay Kumar Khattri

Department of Mathematics, University of Bergen, Bergen 5008, Norway

Received 21 February 2006; Revised 30 May 2006; Accepted 13 June 2006

Copyright © 2006 Sanjay Kumar Khattri. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present a finite volume discretization of the nonlinear elliptic problems. The discretization results in a nonlinear algebraic system of equations. A Newton-Krylov algorithm is also presented for solving the system of nonlinear algebraic equations. Numerically solving nonlinear partial differential equations consists of discretizing the nonlinear partial differential equation and then solving the formed nonlinear system of equations. We demonstrate the convergence of the discretization scheme and also the convergence of the Newton solver through a variety of practical numerical examples.