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<p>We are interested in the problem of identifying the viscosity of a fluid based on observations. This analysis is twofold. First, a stability property of the inverse problem is proved. Secondly, we analyse the discretization of the optimization problem using reduced Hsieh-Clough-Tocher elements, and a convergence with order 3/2 of the identified viscosity with respect to the mesh size is determined. We conclude the paper with some numerical examples showing that this 3/2 order might be enhanced with correct assumptions.</p>

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A priori error estimate for the reduced Hsieh-Clough-Tocher discretization of viscosity identification in Navier–Stokes equations

  • 期刊论文

  • 发表日期：

    2025年11月10日

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  • Alexandre Vieira

摘要

We are interested in the problem of identifying the viscosity of a fluid based on observations. This analysis is twofold. First, a stability property of the inverse problem is proved. Secondly, we analyse the discretization of the optimization problem using reduced Hsieh-Clough-Tocher elements, and a convergence with order 3/2 of the identified viscosity with respect to the mesh size is determined. We conclude the paper with some numerical examples showing that this 3/2 order might be enhanced with correct assumptions.