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A Nitsche-based
cut finite element method for a fluid-structure interaction
problem
André Massing, Mats G. Larson, Anders Logg and Marie E. Rognes |
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Vol. 10 (2015), No. 2, 97–120
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Abstract |
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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. |
Keywords
fluid-structure interaction, overlapping meshes, cut finite
element method, embedded meshes, stabilized finite element
methods, Nitsche's method
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Mathematical Subject Classification 2010
Primary: 65N12, 65N30, 74B20, 76D07, 65N85
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Milestones
Received: 11 November 2013
Revised: 21 February 2015
Accepted: 3 April 2015
Published: 4 September 2015
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Authors |
| André Massing | |
| Department of Mathematics and
Mathematical Statistics Umeå University 901 87 Umeå Sweden |
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| Mats G. Larson | |
| Department of Mathematics and
Mathematical Statistics Umeå University 901 87 Umeå Sweden |
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| Anders Logg | |
| Department of Mathematical
Sciences Chalmers University of Technology 412 96 Göteborg Sweden |
Department of Mathematical
Sciences University of Gothenburg 412 61 Göteborg Sweden |
| Marie E. Rognes | |
| Simula Research Laboratory 1364 Fornebu Norway |
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