NONLINEAR ELLIPTIC PROBLEMS WITH THE METHOD OF FINITE VOLUMES

We present a finite volume discretization of the nonlinear elliptic problems. The dis-cretization results in a nonlinear algebraic system of equations. A Newton-Krylov algo-rithm is also presented for solving the system of nonlinear algebraic equations. Numeri-cally 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. 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. 1