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

Daniele Boffi (), Lucia Gastaldi () and Luca Heltai ()
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Daniele Boffi: Dipartimento di Matematica “F. Casorati”
Lucia Gastaldi: Dipartimento di Matematica
Luca Heltai: Dipartimento di Matematica “F. Casorati”

A chapter in Numerical Mathematics and Advanced Applications, 2006, pp 575-582 from Springer

Abstract: 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.

Date: 2006
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DOI: 10.1007/978-3-540-34288-5_54

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