EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 56 / No 4 (July-August 2022) ESAIM: M2AN, 56 4 (2022) 1307-1326 References
Open Access
Issue
ESAIM: M2AN
Volume 56, Number 4, July-August 2022
Page(s) 1307 - 1326
DOI https://doi.org/10.1051/m2an/2022048
Published online 27 June 2022
  1. L. Baillet and T. Sassi, Mixed finite element methods for the Signorini problem with friction. Numer. Methods Part. Differ. Equ. 22 (2006) 1489–1508. [CrossRef] [Google Scholar]
  2. F. Chouly, An adaptation of Nitsche’s method to the Tresca friction problem. J. Math. Anal. App. 411 (2014) 329–339. [CrossRef] [Google Scholar]
  3. F. Chouly, M. Fabre, P. Hild, R. Mlika, J. Pousin and Y. Renard, An overview of recent results on Nitsche’s method for contact problems. In: Geometrically Unfitted Finite Element Methods and Applications, edited by S.P.A. Bordas, E.N. Burman, M.G. Larson and M.A. Olshanskii. Vol. 121 of Lecture Notes in Computational Science and Engineering. Springer (2017). [Google Scholar]
  4. F. Chouly, M. Fabre, P. Hild, J. Pousin and Y. Renard, Residual-based a posteriori error estimation for contact problems approximated by Nitsche’s method. IMA J. Numer. Anal. 38 (2018) 921–954. [CrossRef] [MathSciNet] [Google Scholar]
  5. 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]
  6. F. Chouly, A. Ern and N. Pignet, A hybrid high-order discretization combined with Nitsche’s method for contact and Tresca friction in small strain elasticity. SIAM J. Sci. Comput. 42 (2020) A2300–A2324. [CrossRef] [Google Scholar]
  7. P. Dörsek and J.M. Melenk, Adaptive hp-FEM for the contact problem with Tresca friction in linear elasticity: the primal-dual formulation and a posteriori error estimation. Appl. Numer. Math. 60 (2010) 689–704. [CrossRef] [MathSciNet] [Google Scholar]
  8. G. Duvaut and J.L. Lions, Inequalities in Mechanics and Physics. Springer, Berlin (1976). [CrossRef] [Google Scholar]
  9. T. Gustafsson, Source code for the numerical experiment: kinnala/paper-fricnitsche. Preprint DOI: 10.5281/zenodo.5851711 (2022). [Google Scholar]
  10. T. Gustafsson and G.D. McBain, scikit-fem: a Python package for finite element assembly. J. Open Source Softw. 5 (2020) 2369. [CrossRef] [Google Scholar]
  11. T. Gustafsson, R. Stenberg and J. Videman, Mixed and stabilized finite element methods for the obstacle problem. SIAM J. Numer. Anal. 55 (2017) 2718–2744. [CrossRef] [MathSciNet] [Google Scholar]
  12. T. Gustafsson, R. Stenberg and J. Videman, On Nitsche’s method for elastic contact problems. SIAM J. Sci. Comput. 42 (2020) B425–B446. [CrossRef] [Google Scholar]
  13. J. Haslinger and I. Hlaváçek, Approximation of the Signorini problem with friction by a mixed finite element method. J. Math. Anal. App. 86 (1982) 99–122. [CrossRef] [Google Scholar]
  14. J. Haslinger and T. Sassi, Mixed finite element approximation of 3D contact problems with given friction: error analysis and numerical realization. ESAIM: Math. Modell. Numer. Anal. 38 (2004) 563–578. [CrossRef] [EDP Sciences] [Google Scholar]
  15. J. Haslinger, I. Hlaváček and J. Nečas, Numerical methods for unilateral problems in solid mechanics. In: Finite Element Methods (Part 2), Numerical Methods for Solids (Part 2). Vol. 4 of Handbook of Numerical Analysis. Elsevier (1996) 313–485. [CrossRef] [Google Scholar]
  16. P. Hild and V. Lleras, Residual error estimators for Coulomb friction. SIAM J. Numer. Anal. 47 (2009) 3550–3583. [CrossRef] [MathSciNet] [Google Scholar]
  17. P. Hild and Y. Renard, An error estimate for the Signorini problem with Coulomb friction approximated by finite elements. SIAM J. Numer. Anal. 45 (2007) 2012–2031. [CrossRef] [MathSciNet] [Google Scholar]
  18. P. Hild and Y. Renard, A stabilized Lagrange multiplier method for the finite element approximation of contact problems in elastostatics. Numer. Math. 115 (2010) 101–129. [CrossRef] [MathSciNet] [Google Scholar]
  19. S. Hüeber, G. Stadler and B.I. Wohlmuth, A primal-dual active set algorithm for three-dimensional contact problems with Coulomb friction. SIAM J. Sci. Comput. 30 (2008) 572–596. [CrossRef] [MathSciNet] [Google Scholar]
  20. J.D. Hunter, Matplotlib: A 2d graphics environment. Comput. Sci. Eng. 9 (2007) 90–95. [NASA ADS] [CrossRef] [Google Scholar]
  21. N. Kikuchi and J.T. Oden, Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods. SIAM, Philadelphia (1988). [CrossRef] [Google Scholar]
  22. P. Laborde and Y. Renard, Fixed point strategies for elastostatic frictional contact problems. Math. Methods Appl. Sci. 31 (2008) 415–441. [CrossRef] [MathSciNet] [Google Scholar]
  23. T.A. Laursen, Computational Contact and Impact Mechanics, corr. 2nd printing. Springer, Heidelberg (2003). [CrossRef] [Google Scholar]
  24. R. Verfürth, A Posteriori Error Estimation Techniques for Finite Element Methods. Oxford University Press, Oxford (2013). [CrossRef] [Google Scholar]
  25. P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K. Jarrod Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt and SciPy 1.0 Contributors, SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nat. Methods 17 (2020) 261–272. [NASA ADS] [CrossRef] [Google Scholar]
  26. B. Wohlmuth, Variationally consistent discretization schemes and numerical algorithms for contact problems. Acta Numer. 20 (2011) 569–734. [CrossRef] [MathSciNet] [Google Scholar]
  27. P. Wriggers, Computational Contact Mechanics, 2nd edition, Springer-Verlag, Berlin Heidelberg (2006). [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you