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<p>We review the main features of an unfitted finite element method for interface and fluid–structure interaction problems based on a distributed Lagrange multiplier in the spirit of the fictitious domain approach. We recall our theoretical findings concerning well-posedness, stability, and convergence of the numerical schemes, and discuss the related computational challenges. In the case of elliptic interface problems, we also present a posteriori error estimates.</p>

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Advances on finite element discretization of fluid–structure interaction problems

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年9月30日

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  • Najwa Alshehri,
  • Daniele Boffi,
  • Fabio Credali,
  • Lucia Gastaldi

摘要

We review the main features of an unfitted finite element method for interface and fluid–structure interaction problems based on a distributed Lagrange multiplier in the spirit of the fictitious domain approach. We recall our theoretical findings concerning well-posedness, stability, and convergence of the numerical schemes, and discuss the related computational challenges. In the case of elliptic interface problems, we also present a posteriori error estimates.