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An H1-Galerkin mixed finite element method for identification of time dependent parameters in parabolic problems

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  • Khebchareon, Morrakot
  • Pany, Ambit Kumar
  • Pani, Amiya K.

Abstract

A direct method of identification of time dependent parameters in a linear parabolic boundary value problem with over-specified total internal energy involves the flux at the boundary, and an H1 mixed formulation seems to be more suitable than the standard methods for such class of nonlocal problems. Therefore, this paper develops and analyses an H1-Galerkin mixed finite element method. Optimal error estimates in both primary and flux variables are derived in semidiscrete case. Moreover, a priori error estimate for the parameters is established. Based on linearised backward Euler method, a completely discrete scheme is proposed and optimal error analysis is derived. The results of the numerical experiments show the efficacy of the proposed method and confirm our theoretical results.

Suggested Citation

  • Khebchareon, Morrakot & Pany, Ambit Kumar & Pani, Amiya K., 2022. "An H1-Galerkin mixed finite element method for identification of time dependent parameters in parabolic problems," Applied Mathematics and Computation, Elsevier, vol. 424(C).
    • Handle: RePEc:eee:apmaco:v:424:y:2022:i:c:s009630032200131x
    DOI: 10.1016/j.amc.2022.127045
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    References listed on IDEAS

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    1. A. K. Pani & P. C. Das, 1987. "An H 1 -Galerkin method for a Stefan problem with a quasilinear parabolic equation in non-divergence form," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 10, pages 1-16, January.
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