NUMERICAL IDENTIFICATION OF A ROBIN COEFFICIENT IN PARABOLIC PROBLEMS

Bangti Jin, Xiliang Lu

Research output: Contribution to journalArticlepeer-review

32 Scopus citations

Abstract

This paper studies a regularization approach for an inverse problem of estimating a spatially-and-temporally dependent Robin coefficient arising in the analysis of convective heat transfer. The parameter-to-state map is analyzed, especially a differentiability result is established. A regularization approach is proposed, and the properties, e.g., existence and optimality system, of the functional are investigated. A finite element method is adopted for discretizing the continuous optimization problem, and the convergence of the finite element approximations as the mesh size and temporal step size tend to zero is established. Numerical results by the conjugate gradient method for one- and two-dimensional problems are presented.
Original languageEnglish (US)
Pages (from-to)1369-1398
Number of pages30
JournalMATHEMATICS OF COMPUTATION
Volume81
Issue number279
DOIs
StatePublished - 2012
Externally publishedYes

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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