Advances on the finite element discretization of fluid-structure interaction problems

2025/05/05 by Alshehri, Najwa, Boffi, Daniele, Credali, Fabio +1 · 2 citations
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2505.02594

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.

Cited by

• A modified Brinkman penalization fictitious domain method for the unsteady Navier-Stokes equations
• Augmented Lagrangian preconditioners for fictitious domain formulations of elliptic interface problems

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