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October 1, 2025Arabian Journal of Mathematics2 citationsOpen Access

Advances on finite element discretization of fluid–structure interaction problems

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NANajwa AlshehriDBDaniele BoffiFCFabio Credali

Key Points

  • The study finds improved stability and convergence in the unfitted finite element method for fluid-structure interaction problems, enhancing computational efficiency.
  • Key theoretical results include well-posedness and a posteriori error estimates, supporting the robustness of the proposed numerical schemes.
  • The method employs a distributed Lagrange multiplier and addresses computational challenges, offering a novel approach based on the fictitious domain method.
  • Findings underline the importance of addressing error estimates for elliptic interface problems in fluid-structure interactions, aiming for enhanced accuracy.

Abstract

Abstract 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.

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Cite This Study

Alshehri et al. (2025) studied this question.

synapsesocial.com/papers/68dd91cffe798ba2fc498ca2https://doi.org/10.1007/s40065-025-00570-8
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