Abstract
In this work we suggest an iterative process for coefficient inverse problem. A parabolic equation in a bounded area supplied with initial condition and monotonic nondecreasing on time Dirichlet condition on a boundary is considered. We state a problem to recover the lowest order coefficient that depends only on spatial variables under an additional information as the observation of a solution taken at the final point of time. For numerical recovering of the coefficient we build the iterative process, at each iteration we perform finite-element approximation in space and fully implicit two-level discretization in time. For capabilities of given iterative process we present computational test for a model problem.
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Funding
The work for the first author was supported by the mega-grant of the Russian Federation Government (N 14.Y26.31.0013), and for the second by the Russian Foundation for Basic Research (project 17-01-00689).
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Ivanov, D.K., Vabishchevich, P.N. (2019). Iterative Process for Numerical Recovering the Lowest Order Space-Wise Coefficient in Parabolic Equations. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Finite Difference Methods. Theory and Applications. FDM 2018. Lecture Notes in Computer Science(), vol 11386. Springer, Cham. https://doi.org/10.1007/978-3-030-11539-5_32
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DOI: https://doi.org/10.1007/978-3-030-11539-5_32
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