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

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.

30 pages, 12 figures, 3 tables

References in corpus (8)

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• Splitting schemes for a Lagrange multiplier formulation of FSI with immersed thin-walled structure: stability and convergence analysis
• A thermo-flow-mechanics-fracture model coupling a phase-field interface approach and thermo-fluid-structure interaction
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• Unfitted mixed finite element methods for elliptic interface problems