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Stability Results and Algorithmic Strategies for the Finite Element Approach to the Immersed Boundary Method

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • Daniele Boffi

    (Dipartimento di Matematica “F. Casorati”)

  • Lucia Gastaldi

    (Dipartimento di Matematica)

  • Luca Heltai

    (Dipartimento di Matematica “F. Casorati”)

Abstract

The immersed boundary method is both a mathematical formulation and a numerical method for the study of fluid structure interactions. Many numerical schemes have been introduced to reduce the difficulties related to the non-linear coupling between the structure and the fluid evolution; however numerical instabilities arise when explicit or semi-implicit methods are considered. In this work we present a stability analysis based on energy estimates for the variational formulation of the immersed boundary method.

Suggested Citation

  • Daniele Boffi & Lucia Gastaldi & Luca Heltai, 2006. "Stability Results and Algorithmic Strategies for the Finite Element Approach to the Immersed Boundary Method," Springer Books, in: Alfredo Bermúdez de Castro & Dolores Gómez & Peregrina Quintela & Pilar Salgado (ed.), Numerical Mathematics and Advanced Applications, pages 575-582, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-34288-5_54
    DOI: 10.1007/978-3-540-34288-5_54
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