The time-fractional diffusion inverse problem subject to an extra measurement by a local discontinuous Galerkin method

This paper deals with an inverse problem of identifying a space dependent coefficient in a time-fractional diffusion equation on a finite domain with final observation. The existence and uniqueness of this inverse problem are proved. A numerical scheme is proposed to solve the problem. The main idea...

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Bibliographic Details
Published inBIT Vol. 59; no. 1; pp. 183 - 212
Main Authors Qasemi, Samaneh, Rostamy, Davood, Abdollahi, Nazdar
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 04.03.2019
Springer Nature B.V
Subjects
Computational Mathematics and Numerical Analysis
Galerkin method
Inverse problems
Mathematical analysis
Mathematics
Mathematics and Statistics
Numeric Computing
Time dependence
65M15
Riemann–Liouville derivative
Error estimate
76M60
65M12
Existence and uniqueness
Inverse problem
Local discontinuous Galerkin method
65M32
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Summary:This paper deals with an inverse problem of identifying a space dependent coefficient in a time-fractional diffusion equation on a finite domain with final observation. The existence and uniqueness of this inverse problem are proved. A numerical scheme is proposed to solve the problem. The main idea of the proposed scheme is approximating the time fractional derivative by Diethelm’s quadrature formula and use the local discontinuous Galerkin method in space variable. Also, an error estimate for this problem is presented. Finally, two numerical example is studied to demonstrate the accuracy and efficiency of the proposed method.
Bibliography:ObjectType-Article-1
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content type line 14
ISSN:0006-3835
1572-9125
DOI:10.1007/s10543-018-0731-z