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

被引：0
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作者：
Daijun Jiang
Yikan Liu
Dongling Wang
机构：
[1] Central China Normal University,School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences
[2] Hokkaido University,Research Center of Mathematics for Social Creativity, Research Institute for Electronic Science
[3] Northwest University,Department of Mathematics and Center for Nonlinear Studies
来源：
Advances in Computational Mathematics | 2020年 / 46卷
关键词：
Time-fractional diffusion equation; Inverse source problem; Finite element method; Iterative thresholding algorithm; 35R11; 65M32; 41A35;
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摘要：
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 H1-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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