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A Distributed Lagrange Formulation of the Finite Element Immersed Boundary Method for Fluids Interacting with Compressible Solids

  • Daniele BoffiEmail author
  • Lucia Gastaldi
  • Luca Heltai
Chapter
Part of the SEMA SIMAI Springer Series book series (SEMA SIMAI, volume 16)

Abstract

We present a distributed Lagrange multiplier formulation of the Finite Element Immersed Boundary Method to couple incompressible fluids with compressible solids. This is a generalization of the formulation presented in Heltai and Costanzo (Comput. Methods Appl. Mech. Eng. 229/232:110–127, 2012), that offers a cleaner variational formulation, thanks to the introduction of distributed Lagrange multipliers, that act as intermediary between the fluid and solid equations, keeping the two formulation mostly separated. Stability estimates and a brief numerical validation are presented.

Notes

Acknowledgements

This work has been partly supported by IMATI/CNR and GNCS/INDAM.

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Dipartimento di Matematica “F. Casorati”Università di PaviaPaviaItaly
  2. 2.Department of Mathematics and System AnalysisAalto UniversityHelsinkiFinland
  3. 3.DICATAMUniversità di BresciaBresciaItaly
  4. 4.SISSATriesteItaly

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