Nonlinear elliptic problems with the method of finite volumes

Khattri, Sanjay Kumar

doi:https://doi.org/10.1155/DENM/2006/31797

International Journal of Differential Equations

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Volume 2006 | Article ID 031797 | https://doi.org/10.1155/DENM/2006/31797

Nonlinear elliptic problems with the method of finite volumes

Sanjay Kumar Khattri¹

Received21 Feb 2006

Revised30 May 2006

Accepted13 Jun 2006

Published19 Oct 2006

Abstract

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.

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Copyright

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.

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