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

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Imam Khomeini International University, Qazvin, Iran

    Samaneh Qasemi, Davood Rostamy & Nazdar Abdollahi

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  1. Samaneh Qasemi
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  2. Davood Rostamy
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  3. Nazdar Abdollahi
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Correspondence to Samaneh Qasemi.

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Communicated by Jan Hesthaven.

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Qasemi, S., Rostamy, D. & Abdollahi, N. The time-fractional diffusion inverse problem subject to an extra measurement by a local discontinuous Galerkin method. Bit Numer Math 59, 183–212 (2019). https://doi.org/10.1007/s10543-018-0731-z

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  • DOI: https://doi.org/10.1007/s10543-018-0731-z

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