Free Access
Issue
ESAIM: M2AN
Volume 54, Number 2, March-April 2020
Page(s) 531 - 564
DOI https://doi.org/10.1051/m2an/2019072
Published online 18 February 2020
  1. P. Alart and A. Curnier, A mixed formulation for frictional contact problems prone to Newton like solution methods. Comput. Methods Appl. Mech. Eng. 92 (1991) 353–375. [Google Scholar]
  2. F. Alauzet, B. Fabréges, M.A. Fernández and M. Landajuela, Nitsche-XFEM for the coupling of an incompressible fluid with immersed thin-walled structures. Comput. Methods Appl. Mech. Eng. 301 (2016) 300–335. [Google Scholar]
  3. P. Angot, Analysis of singular perturbations on the brinkman problem for fictitious domain models of viscous flows. Math. Methods Appl. Sci. 22 (1999) 1395–1412. [Google Scholar]
  4. M. Astorino, J.F. Gerbeau, O. Pantz and K.F. Traoré, Fluid-structure interaction and multi-body contact: application to aortic valves. Comput. Methods Appl. Mech. Eng. 198 (2009) 3603–3612. [Google Scholar]
  5. R. Becker and M. Braack, A finite element pressure gradient stabilization for the Stokes equations based on local projections. Calcolo 38 (2001) 173–199. [CrossRef] [MathSciNet] [Google Scholar]
  6. R. Becker, M. Braack, D. Meidner, T. Richter and B. Vexler. The finite element toolkit Gascoigne3d. http://www.gascoigne.uni-hd.de. [Google Scholar]
  7. M. Besier and W. Wollner, On the pressure approximation in nonstationary incompressible flow simulations on dynamically varying spatial meshes. Int. J. Numer. Methods Fluids 69 (2012) 1045–1064. [Google Scholar]
  8. D. Boffi and L. Gastaldi, A finite element approach for the immersed boundary method. Comput. Struct. 81 (2003) 491–501. [Google Scholar]
  9. L. Boilevin-Kayl, M.A. Fernández and J.F. Gerbeau, Numerical methods for immersed fsi with thin-walled structures. Comput. Fluids 179 (2019) 744–763. [Google Scholar]
  10. F. Brezzi and J. Pitkäranta, On the stabilization of finite element approximations of the stokes equations, edited by W. Hackbusch. In: Efficient Solutions of Elliptic Systems. Springer (1984) 11–19. [CrossRef] [Google Scholar]
  11. V. Bruyere, N. Fillot, G.E. Morales-Espejel and P. Vergne, Computational fluid dynamics and full elasticity model for sliding line thermal elastohydrodynamic contacts. Tribol. Int. 46 (2012) 3–13. [Google Scholar]
  12. E. Burman, Ghost penalty. C.R. Math. 348 (2010) 1217–1220. [CrossRef] [MathSciNet] [Google Scholar]
  13. E. Burman and M.A. Fernández, An unfitted Nitsche method for incompressible fluid–structure interaction using overlapping meshes. Comput. Methods Appl. Mech. Eng. 279 (2014) 497–514. [Google Scholar]
  14. E. Burman and P. Hansbo, Edge stabilization for the generalized Stokes problem: a continuous interior penalty method. Comput. Methods Appl. Mech. Eng. 195 (2006) 2393–2410. [Google Scholar]
  15. E. Burman and P. Hansbo, Fictitious domain finite element methods using cut elements: II. A stabilized Nitsche method. Appl. Numer. Math. 62 (2012) 328–341. [Google Scholar]
  16. E. Burman and P. Hansbo, Deriving robust unfitted finite element methods from augmented lagrangian formulations, edited by S.P.A. Bordas, E. Burman, M.G. Larson and M.A. Olshanskii. In: Geometrically Unfitted Finite Element Methods and Applications – Proceedings of the UCL-workshop 2016. Springer (2017) 1–24. [Google Scholar]
  17. E. Burman, P. Hansbo, M.G. Larson and R. Stenberg, Galerkin least squares finite element method for the obstacle problem. Comput. Methods Appl. Mech. Eng. 313 (2017) 362–374. [Google Scholar]
  18. E. Burman, P. Hansbo and M.G. Larson, Augmented lagrangian and galerkin least-squares methods for membrane contact. Int. J. Numer. Methods Eng. 114 (2018) 1179–1191. [Google Scholar]
  19. F. Chouly, An adaptation of Nitsche’s method to the tresca friction problem. J. Math. Anal. Appl. 411 (2014) 329–339. [Google Scholar]
  20. F. Chouly and P. Hild, A Nitsche-based method for unilateral contact problems: numerical analysis. SIAM J. Numer. Anal. 51 (2013) 1295–1307. [Google Scholar]
  21. F. Chouly, P. Hild and Y. Renard, A Nitsche finite element method for dynamic contact: 1. space semi-discretization and time-marching schemes. ESAIM: M2AN 49 (2015) 481–502. [CrossRef] [EDP Sciences] [Google Scholar]
  22. F. Chouly, P. Hild and Y. Renard, Symmetric and non-symmetric variants of Nitsche’s method for contact problems in elasticity: Theory and numerical experiments. Math. Comput. 84 (2015) 1089–1112. [Google Scholar]
  23. F. Chouly, R. Mlika and Y. Renard, An unbiased Nitsche’s approximation of the frictional contact between two elastic structures. Numer. Math. 139 (2018) 593–631. [Google Scholar]
  24. F. Chouly, P. Hild, V. Lleras and Y. Renard, Nitsche-based finite element method for contact with coulomb friction, edited by F.A. Radu, K. Kumar, I. Berre, J.M. Nordbotten and I.S. Pop. In: Numerical Mathematics and Advanced Applications ENUMATH 2017. Springer International Publishing (2019) 839–847. [CrossRef] [Google Scholar]
  25. F. Cimolin and M. Discacciati, Navier–Stokes/Forchheimer models for filtration through porous media. Appl. Numer. Math. 72 (2013) 205–224. [Google Scholar]
  26. G.H. Cottet, E. Maitre and T. Milcent, Eulerian formulation and level set models for incompressible fluid-structure interaction. ESAIM: M2AN 42 (2008) 471–492. [CrossRef] [EDP Sciences] [Google Scholar]
  27. N.D. dos Santos, J.F. Gerbeau and J.F. Bourgat, A partitioned fluid–structure algorithm for elastic thin valves with contact. Comput. Methods Appl. Mech. Eng. 197 (2008) 1750–1761. [Google Scholar]
  28. T. Dunne, Adaptive finite element approximation of fluid-structure interaction based on Eulerian and Arbitrary Lagrangian-Eulerian variational formulations. Ph.D. thesis, Heidelberg University (2007). [Google Scholar]
  29. T. Dunne and R. Rannacher, Adaptive finite element approximation of fluid-structure interaction based on an Eulerian variational formulation, edited by H.J. Bungartz and M. Schäfer. In: Fluid-Structure Interaction: Modeling, Simulation, Optimization. Lect. Notes Comput. Sci. Eng. Springer (2006) 110–145. [CrossRef] [Google Scholar]
  30. S. Frei, Eulerian finite element methods for interface problems and fluid-structure interactions. Ph.D. thesis, Heidelberg University (2016) http://www.ub.uni-heidelberg.de/archiv/21590. [Google Scholar]
  31. S. Frei, An edge-based pressure stabilization technique for finite elements on arbitrarily anisotropic meshes. Int. J. Numer. Methods Fluids 89 (2019) 407–429. [Google Scholar]
  32. S. Frei and T. Richter, A locally modified parametric finite element method for interface problems. SIAM J. Numer. Anal. 52 (2014) 2315–2334. [MathSciNet] [Google Scholar]
  33. S. Frei and T. Richter, An accurate Eulerian approach for fluid-structure interactions, edited by S. Frei, B. Holm, T. Richter, T. Wick and H. Yang. In: Fluid-Structure Interaction: Modeling, Adaptive Discretization and Solvers. Rad. Ser. Comput. Appl. Math. Walter de Gruyter, Berlin (2017). [CrossRef] [Google Scholar]
  34. S. Frei and T. Richter, A second order time-stepping scheme for parabolic interface problems with moving interfaces. ESAIM: M2AN 51 (2017) 1539–1560. [CrossRef] [EDP Sciences] [Google Scholar]
  35. D. Gérard-Varet and M. Hillairet, Regularity issues in the problem of fluid structure interaction. Arch. Ration Mech. Anal. 195 (2010) 375–407. [Google Scholar]
  36. D. Gerard-Varet, M. Hillairet and C. Wang, The influence of boundary conditions on the contact problem in a 3D Navier-Stokes flow. J. Math. Pure Appl. 103 (2015) 1–38. [CrossRef] [Google Scholar]
  37. A. Gerstenberger and W.A. Wall, An extended finite element method/Lagrange multiplier based approach for fluid–structure interaction. Comput. Methods Appl. Mech. Eng. 197 (2008) 1699–1714. [Google Scholar]
  38. C. Grandmont and M. Hillairet, Existence of global strong solutions to a beam–fluid interaction system. Arch. Ration Mech. Anal. 220 (2016) 1283–1333. [Google Scholar]
  39. C. Grandmont, M. Lukáčová-Medvidóvá and Š. Nečasová, Mathematical and numerical analysis of some FSI problems, edited by T. Bodnár, G.P. Galdi, Š. Nečasová. In: Fluid-Structure Interaction and Biomedical Applications. Springer (2014) 1–77. [Google Scholar]
  40. P. Hansbo, J. Hermansson and T. Svedberg, Nitsche’s method combined with space–time finite elements for ALE fluid–structure interaction problems. Comput. Methods Appl. Mech. Eng. 193 (2004) 4195–4206. [Google Scholar]
  41. F. Hecht and O. Pironneau, An energy stable monolithic eulerian fluid-structure finite element method. Int. J. Numer. Methods Fluids 85 (2017) 430–446. [Google Scholar]
  42. T.I. Hesla, Collisions of smooth bodies in viscous fluids: A mathematical investigation Ph.D. thesis, Univ. of Minnesota (2004). [Google Scholar]
  43. M. Hillairet, Lack of collision between solid bodies in a 2D incompressible viscous flow. Commun. Part Diff. Equ. 32 (2007) 1345–1371. [CrossRef] [MathSciNet] [Google Scholar]
  44. M. Hillairet and T. Takahashi, Collisions in three-dimensional fluid structure interaction problems. SIAM J. Math. Anal. 40 (2009) 2451–2477. [CrossRef] [Google Scholar]
  45. M. Hintermüller, K. Ito and K. Kunisch, The primal-dual active set strategy as a semismooth newton method. SIAM J. Opt. 13 (2002) 865–888. [CrossRef] [MathSciNet] [Google Scholar]
  46. S. Hüeber and B.I. Wohlmuth, A primal–dual active set strategy for non-linear multibody contact problems. Comput. Methods Appl. Mech. Eng. 194 (2005) 3147–3166. [Google Scholar]
  47. T.J.R. Hughes, L.P. Franca and M. Balestra, A new finite element formulation for computational fluid dynamics: V. circumventing the Babuška-Brezzi condition: a stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations. Comput. Methods Appl. Mech. Eng. 59 (1986) 85–99. [Google Scholar]
  48. O. Iliev and V. Laptev, On numerical simulation of flow through oil filters. Comput. Visu. Sci. 6 (2004) 139–146. [CrossRef] [Google Scholar]
  49. D. Kamensky, M.C. Hsu, D. Schillinger, J.A. Evans, A. Aggarwal, Y. Bazilevs, M.S. Sacks and T.J.R. Hughes, An immersogeometric variational framework for fluid–structure interaction: Application to bioprosthetic heart valves. Comput. Methods Appl. Mech. Eng. 284 (2015) 1005–1053. [CrossRef] [PubMed] [Google Scholar]
  50. S. Knauf, S. Frei, T. Richter and R. Rannacher, Towards a complete numerical description of lubricant film dynamics in ball bearings. Comput. Mech. 53 (2014) 239–255. [Google Scholar]
  51. A. Legay, J. Chessa and T. Belytschko, An Eulerian-Lagrangian method for fluid-structure interaction based on level sets. Comput. Methods Appl. Mech. Eng. 195 (2006) 2070–2087. [Google Scholar]
  52. S. Mandal, A. Ouazzi and S. Turek, Modified newton solver for yield stress fluids, edited by B. Karasözen, M. Manguoğlu, M. Tezer-Sezgin, S. Göktepe and Ö. Uğur. In: Numerical Mathematics and Advanced Applications ENUMATH 2015. Springer International Publishing (2016) 481–490. [CrossRef] [Google Scholar]
  53. A. Massing, M. Larson, A. Logg and M. Rognes, A nitsche-based cut finite element method for a fluid-structure interaction problem. Comm. Appl. Math. Comput. Sci. 10 (2015) 97–120. [CrossRef] [Google Scholar]
  54. U.M. Mayer, A. Popp, A. Gerstenberger and W.A. Wall, 3D fluid–structure-contact interaction based on a combined XFEM FSI and dual mortar contact approach. Comput. Mech. 46 (2010) 53–67. [Google Scholar]
  55. R. Mlika, Y. Renard and F. Chouly, An unbiased Nitsche’s formulation of large deformation frictional contact and self-contact. Comput. Methods Appl. Mech. Eng. 325 (2017) 265–288. [Google Scholar]
  56. B. Muha and S. Čanić, Existence of a weak solution to a fluid-elastic structure interaction problem with the Navier slip boundary condition. J. Diff. Equ. 260 (2016) 8550–8589. [CrossRef] [Google Scholar]
  57. J.A. Nitsche, Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. Abh. Math. Univ. Hamburg 36 (1970) 9–15. [CrossRef] [MathSciNet] [Google Scholar]
  58. C.S. Peskin, Flow patterns around heart valves: a numerical method. J. Comput. Phys. 10 (1972) 252–271. [Google Scholar]
  59. K. Poulios and Y. Renard, An unconstrained integral approximation of large sliding frictional contact between deformable solids. Comput. Struct. 153 (2015) 75–90. [Google Scholar]
  60. M.A. Puso, A 3D mortar method for solid mechanics. Int. J. Numer. Methods Eng. 59 (2004) 315–336. [Google Scholar]
  61. T. Richter, A fully Eulerian formulation for fluid-structure interactions. J. Comput. Phys. 233 (2013) 227–240. [Google Scholar]
  62. T. Richter, Finite elements for fluid-structure interactions. models, analysis and finite elements. In: Vol. 118 of Lect Notes Comput. Sci. Eng. Springer (2017). [CrossRef] [Google Scholar]
  63. T.E. Tezduyar and S. Sathe, Modeling of fluid-structure interactions with the space-time finite elements: solution techniques. Int. J. Numer. Methods Fluids 54 (2007) 855–900. [Google Scholar]
  64. C. Wang, Strong solutions for the fluid–solid systems in a 2-D domain. Asymptotic Anal. 89 (2014) 263–306. [CrossRef] [Google Scholar]
  65. B. Wohlmuth, Variationally consistent discretization schemes and numerical algorithms for contact problems. Acta Numer. 20 (2011) 569–734. [CrossRef] [Google Scholar]
  66. B. Yang, T.A. Laursen and X. Meng, Two dimensional mortar contact methods for large deformation frictional sliding. Int. J. Numer. Methods Eng. 62 (2005) 1183–1225. [Google Scholar]
  67. L. Zhang, A. Gerstenberger, X. Wang and W.K. Liu, Immersed finite element method. Comput. Methods Appl. Mech. Eng. 193 (2004) 2051–2067. [Google Scholar]

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