Table of Contents
International Journal of Partial Differential Equations
Volume 2013, Article ID 590737, 6 pages
http://dx.doi.org/10.1155/2013/590737
Research Article

A Posteriori Regularization Parameter Choice Rule for Truncation Method for Identifying the Unknown Source of the Poisson Equation

School of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, China

Received 30 April 2013; Accepted 19 August 2013

Academic Editor: Athanasios N. Yannacopoulos

Copyright © 2013 Xiao-Xiao Li and Dun-Gang Li. 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.

Abstract

We consider the problem of determining an unknown source which depends only on one variable in two-dimensional Poisson equation. We prove a conditional stability for this problem. Moreover, we propose a truncation regularization method combined with an a posteriori regularization parameter choice rule to deal with this problem and give the corresponding convergence estimate. Numerical results are presented to illustrate the accuracy and efficiency of this method.