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2015 A Nitsche-based cut finite element method for a fluid-structure interaction problem
André Massing, Mats Larson, Anders Logg, Marie Rognes
Commun. Appl. Math. Comput. Sci. 10(2): 97-120 (2015). DOI: 10.2140/camcos.2015.10.97

Abstract

We present a new composite mesh finite element method for fluid-structure interaction problems. The method is based on surrounding the structure by a boundary-fitted fluid mesh that is embedded into a fixed background fluid mesh. The embedding allows for an arbitrary overlap of the fluid meshes. The coupling between the embedded and background fluid meshes is enforced using a stabilized Nitsche formulation that allows us to establish stability and optimal-order a priori error estimates. We consider here a steady state fluid-structure interaction problem where a hyperelastic structure interacts with a viscous fluid modeled by the Stokes equations. We evaluate an iterative solution procedure based on splitting and present three-dimensional numerical examples.

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André Massing. Mats Larson. Anders Logg. Marie Rognes. "A Nitsche-based cut finite element method for a fluid-structure interaction problem." Commun. Appl. Math. Comput. Sci. 10 (2) 97 - 120, 2015. https://doi.org/10.2140/camcos.2015.10.97

Information

Received: 11 November 2013; Revised: 21 February 2015; Accepted: 3 April 2015; Published: 2015
First available in Project Euclid: 16 November 2017

zbMATH: 1326.74122
MathSciNet: MR3402347
Digital Object Identifier: 10.2140/camcos.2015.10.97

Subjects:
Primary: 65N12, 65N30, 65N85, 74B20, 76D07

Rights: Copyright © 2015 Mathematical Sciences Publishers

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