Stabilized explicit coupling for fluid-structure interaction using Nitsche's method

Comptes Rendus Mathematique

Volumn 345, Issue 8, 2007, Pages 467-472

  Burman, Erik ^a   Fernández, Miguel A ^b  

^a EPFL   (Switzerland)

^b INRIA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 36248955552     PISSN: 1631073X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crma.2007.09.010     Document Type: Article

References (17)

1. Becker R., Hansbo P., and Stenberg R. A finite element method for domain decomposition with non-matching grids. M2AN Math. Model. Numer. Anal. 37 2 (2003) 209-225
2. E. Burman, M.A. Fernández, Stabilization of explicit coupling in fluid-structure interaction with fluid incompressibility, in preparation
3. Burman E., and Hansbo P. A unified stabilized method for Stokes' and Darcy's equations. J. Comput. Appl. Math. 198 (2007) 35-51
4. Burman E., and Zunino P. A domain decomposition method based on interior penalties for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 44 (2006) 1612-1638
5. Causin P., Gerbeau J.-F., and Nobile F. Added-mass effect in the design of partitioned algorithms for fluid-structure problems. Comput. Methods Appl. Mech. Engrg. 194 42-44 (2005) 4506-4527
6. Farhat C., van der Zee K., and Geuzaine Ph. Provably second-order time-accurate loosely-coupled solution algorithms for transient nonlinear aeroelasticity. Comput. Methods Appl. Mech. Engrg. 195 17-18 (2006) 1973-2001
7. Fernández M.A., Gerbeau J.F., and Grandmont C. A projection semi-implicit scheme for the coupling of an elastic structure with an incompressible fluid. Int. J. Numer. Methods Engrg. 69 4 (2007) 794-821
8. Fernández M.A., and Moubachir M. A Newton method using exact Jacobians for solving fluid-structure coupling. Comp. & Struct. 83 (2005) 127-142
9. Gerbeau J.-F., and Vidrascu M. A quasi-Newton algorithm based on a reduced model for fluid-structure interactions problems in blood flows. Math. Model. Numer. Anal. 37 4 (2003) 631-648
10. Hansbo P., and Hermansson J. Nitsche's method for coupling non-matching meshes in fluid-structure vibration problems. Comput. Mech. 32 1-2 (2003) 134-139
11. Hansbo P., Hermansson J., and Svedberg T. Nitsche's method combined with space-time finite elements for ALE fluid-structure interaction problems. Comput. Methods Appl. Mech. Engrg. 193 (2004) 4195-4206
12. F. Hecht, O. Pironneau, A. Le Hyaric, K. Ohtsuka, FreeFem++ v. 2.11. User's Manual, University of Paris 6
13. Le Tallec P., and Mouro J. Fluid structure interaction with large structural displacements. Comput. Methods Appl. Mech. Engrg. 190 (2001) 3039-3067
14. Mok D.P., Wall W.A., and Ramm E. Accelerated iterative substructuring schemes for instationary fluid-structure interaction. In: Bathe K.J. (Ed). Computational Fluid and Solid Mechanics (2001), Elsevier 1325-1328
15. Nitsche J. Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. Abh. Math. Sem. Univ. Hamburg 36 (1971) 9-15
16. F. Nobile, Numerical approximation of fluid-structure interaction problems with application to haemodynamics, PhD thesis, EPFL, Switzerland, 2001
17. Stetter H.J. The defect correction principle and discretization methods. Numer. Math. 29 (1978) 425-443