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Advances on the finite element discretization of fluid-structure interaction problems (2505.02594v1)
Published 5 May 2025 in math.NA and cs.NA
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-posedeness, 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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