Differential Equations and Nonlinear Mechanics
Volume 2006 (2006), Article ID 31797, 16 pages
Nonlinear elliptic problems with the method of finite volumes
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.