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

Jiang, Daijun; Liu, Yikan; Wang, Dongling

Advances in Computational Mathematics, 2020, 46(3), 43

Permalink : https://hdl.handle.net/2115/78716

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https://arxiv.org/abs/1812.04235     15

論文情報

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アクセス権
open access
URI
https://hdl.handle.net/2115/78716
タイトル
Numerical reconstruction of the spatial component in the source term of a time-fractional diffusion equation
著者
Jiang, Daijun ; Liu, Yikan ; Wang, Dongling
著者名
Jiang, Daijun
e-Rad_Researcher
70773084
著者名
Liu, Yikan
著者名
Wang, Dongling
言語
英語
キーワード
Time-fractional diffusion equation
Inverse source problem
Finite element method
Iterative thresholding algorithm
発行日
2020-05-04
出版者
Springer
収録物名
Advances in Computational Mathematics
巻(号)
46(3)
ページ
43
抄録
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.
資源タイプ
学術雑誌論文
出版タイプ
Accepted Manuscript
PISSN
1019-7168
関連情報 (isVersionOf)
出版社版DOI
https://doi.org/10.1007/s10444-020-09754-6
URI
https://arxiv.org/abs/1812.04235