Numerical reconstruction of the spatial component in the source term of a time-fractional diffusion equation

In this article, we are concerned with the analysis on the numerical reconstruction of the spatial component in the source term of a time-fractional diffusion equation. This ill-posed problem is solved through a stabilized nonlinear minimization system by an appropriately selected Tikhonov regulariz...

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Bibliographic Details
Published in:Advances in computational mathematics Vol. 46; no. 3
Main Authors: Jiang, Daijun, Liu, Yikan, Wang, Dongling
Format: Journal Article
Language:English
Published: New York Springer US 01.06.2020
Springer Nature B.V
Subjects:
Algorithms
Computational mathematics
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Ill posed problems
Iterative methods
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Optimization
Reconstruction
Regularization
Visualization
Finite element method
41A35
Inverse source problem
35R11
Iterative thresholding algorithm
Time-fractional diffusion equation
65M32
ISSN:1019-7168, 1572-9044
Online Access:Get full text
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Summary:In this article, we are concerned with the analysis on the numerical reconstruction of the spatial component in the source term of a time-fractional diffusion equation. This ill-posed problem is solved through a stabilized nonlinear minimization system by an appropriately selected Tikhonov regularization. The existence and the stability of the optimization system are demonstrated. The nonlinear optimization problem is approximated by a fully discrete scheme, whose convergence is established under a novel result verified in this study that the H 1 -norm of the solution to the discrete forward system is uniformly bounded. The iterative thresholding algorithm is proposed to solve the discrete minimization, and several numerical experiments are presented to show the efficiency and the accuracy of the algorithm.
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ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-020-09754-6