A Directly Numerical Algorithm for a Backward Time-Fractional Diffusion Equation Based on the Finite Element Method. (25th March 2015)

• Record Type: Journal Article
• Authors: Ruan, Zhousheng; Wang, Zewen; Zhang, Wen
• Other Names: Yakhno Valery G. Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2015(2015)
• Publication Date: 2015-03-25
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2015/414727
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : We study a backward problem for a time-fractional diffusion equation, which is formulated into a regularized optimization problem. After solving a sequence of well-posed direct problems by the finite element method, a directly numerical algorithm is proposed for solving the regularized optimization problem. In order to obtain a reasonable regularization solution, we utilize the discrepancy principle with decreasing geometric sequence to choose regularization parameters. One- and two-dimensional examples are given to verify the efficiency and stability of the proposed method.