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Iterative Process for Numerical Recovering the Lowest Order Space-Wise Coefficient in Parabolic Equations

  • D. Kh. IvanovEmail author
  • P. N. Vabishchevich
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11386)

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.

Keywords

Inverse problem Parabolic equation Finite element method Implicit scheme 

Notes

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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Mathematics and Information ScienceNorth-Eastern Federal UniversityYakutskRussia
  2. 2.Nuclear Safety InstituteRussian Academy of SciencesMoscowRussia

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