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February 2026

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Analysis Seminar Announcement - "Non-matching coupling in fluid–structure interaction: constraints, singular forcing, and dimensional reduction" - Luca Heltai
by Fabio Durastante 16 Feb '26

16 Feb '26

Dear Everybody, Please find attached the announcement for an upcoming seminar by Luca Heltai on topics at the intersection of Analysis and Numerical Analysis. This seminar is part of the Analysis seminar series and may be of interest to many of you. Web announcement: https://www.dm.unipi.it/seminario/?id=698b2491dd82ea23a81f8461 Best regards, Fabio * Analysis Seminar: *Non-matching coupling in fluid–structure interaction: constraints, singular forcing, and dimensional reduction *Speaker: *Luca Heltai *Location: *18/02/2026 - 10.00-11.00, Aula Magna (Department of Mathematics) *Abstract.* Fluid–structure interaction problems often involve coupling conditions imposed on interfaces whose geometry is complex, thin, or evolving in time. In many relevant regimes, enforcing such conditions on matching discretizations is either impractical or conceptually inadequate, motivating the use of non-matching and immersed formulations. In this talk, we present an analytical overview of non-matching coupling methods for fluid–structure interaction, interpreting interface conditions as functional constraints, imposed on sets of varying dimensions. We focus on Lagrange multiplier formulations (classical, distributed, and reduced) and discuss their well-posedness and stability properties at both the continuous and discrete levels. A central theme of the talk is the analysis of singular forcing terms generated by non-matching constraints. On the one hand, variational formulations of non-matching coupling typically induce a loss of global regularity in the solution. We show that this loss is in fact a purely local phenomenon, and we characterize it using weighted Sobolev spaces, thereby recovering optimal approximation properties away from the interface. On the other hand, non-matching fluid–structure interaction formulations can be reinterpreted as Navier–Stokes-type problems with singular forcing terms. While classical Immersed Boundary Methods employ regularized Dirac distributions primarily for implementation purposes, we provide a general framework showing that regularization and analysis are not separate issues. In particular, we establish a rigorous connection between regularized and variational formulations, proving that suitably chosen regularizations lead to equivalent finite element approximations, with comparable accuracy and computational cost. We then address dimensional reduction strategies for slender or thin structures, showing how mixed-dimensional models naturally arise as asymptotic limits of non-matching coupling formulations. We discuss how reduced Lagrange multiplier spaces can be designed to preserve well-posedness and stability uniformly with respect to vanishing geometric scales. The presented results provide a unified functional-analytic perspective on a class of non-matching methods used in fluid–structure interaction and related problems, highlighting the mechanisms underlying their stability, accuracy, and robustness across dimensions.

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