A Posteriori Regularization Parameter Choice Rule for Truncation Method for Identifying the Unknown Source of the Poisson Equation. (19th September 2013)

• Record Type: Journal Article
• Authors: Li, Xiao-Xiao; Li, Dun-Gang
• Other Names: Yannacopoulos Athanasios N. Academic Editor.
• Is Part Of: International journal of partial differential equations. Volume 2013 (2013)
• Publication Date: 2013-09-19
• Subjects: Differential equations, Partial -- Periodicals; Differential equations, Partial; Periodicals; 515.353
• DOI: 10.1155/2013/590737
• Languages: English
• ISSNs: 2356-7082

Abstract

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.