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<p>This paper presents a convergence analysis of an iterative algorithm designed to solve a nonlinear inverse heat conduction problem, in which surface temperature is estimated from interior measurements. As this type of problem is inherently ill-posed in practical applications, stability is achieved using the Tikhonov regularization method. While the algorithm was previously introduced in our earlier work (Ngendahayo et al. in Results Appl Math 9(100140):2021, 2021), a rigorous convergence analysis was not provided. In this study, we improve the algorithm by establishing sufficient conditions on the coefficients in the model equation to ensure that the associated nonlinear operator equation is well-defined. We then provide a detailed mathematical analysis of its convergence. The results confirm that the algorithm works as a convergent regularization method. Additionally, numerical examples demonstrate that the algorithm performs effectively, exhibiting rapid convergence.</p>

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Convergence Analysis of Iterative Tikhonov Regularization Applied to an Inverse Heat Conduction Problem

  • 期刊论文

  • 发表日期：

    2025年7月23日

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  • Jean Pierre Ngendahayo,
  • Froduald Minani,
  • Johan Thim,
  • Fredrik Berntsson

摘要

This paper presents a convergence analysis of an iterative algorithm designed to solve a nonlinear inverse heat conduction problem, in which surface temperature is estimated from interior measurements. As this type of problem is inherently ill-posed in practical applications, stability is achieved using the Tikhonov regularization method. While the algorithm was previously introduced in our earlier work (Ngendahayo et al. in Results Appl Math 9(100140):2021, 2021), a rigorous convergence analysis was not provided. In this study, we improve the algorithm by establishing sufficient conditions on the coefficients in the model equation to ensure that the associated nonlinear operator equation is well-defined. We then provide a detailed mathematical analysis of its convergence. The results confirm that the algorithm works as a convergent regularization method. Additionally, numerical examples demonstrate that the algorithm performs effectively, exhibiting rapid convergence.