Review highlights well-posedness and convergence in finite element methods for fluid-structure interaction problems, suggesting advancements in computational techniques.
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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Alshehri et al. (2025) studied this question.
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