Free Access
Volume 41, Number 5, September-October 2007
Page(s) 897 - 923
Published online 23 October 2007
  1. R.A. Adams, Sobolev spaces. Academic Press (1975). [Google Scholar]
  2. K. Atkinson and W. Han, Theoretical numerical analysis: a functional analysis framework, in Texts in Applied Mathematics 39, Springer, New-York (2001); (second edition 2005). [Google Scholar]
  3. F. Ben Belgacem, Numerical simulation of some variational inequalities arisen from unilateral contact problems by the finite element method. SIAM J. Numer. Anal. 37 (2000) 1198–1216. [CrossRef] [MathSciNet] [Google Scholar]
  4. F. Ben Belgacem and Y. Renard, Hybrid finite element methods for the Signorini problem. Math. Comp. 72 (2003) 1117–1145. [CrossRef] [MathSciNet] [Google Scholar]
  5. V. Bostan, W. Han and B.D. Reddy, A posteriori error estimation and adaptive solution of elliptic variational inequalities of the second kind. Appl. Numer. Math. 52 (2005) 13–38. [CrossRef] [MathSciNet] [Google Scholar]
  6. D. Braess, A posteriori error estimators for obstacle problems - another look. Numer. Math. 101 (2005) 415–421. [CrossRef] [MathSciNet] [Google Scholar]
  7. C. Carstensen, O. Scherf and P. Wriggers, Adaptive finite elements for elastic bodies in contact. SIAM J. Sci. Comput. 20 (1999) 1605–1626. [CrossRef] [MathSciNet] [Google Scholar]
  8. Z. Chen and R.H. Nochetto, Residual type a posteriori error estimates for elliptic obstacle problems. Numer. Math. 84 (2000) 527–548. [CrossRef] [MathSciNet] [Google Scholar]
  9. P.G. Ciarlet, The finite element method for elliptic problems, in Handbook of Numerical Analysis, Volume II, Part 1, P.G. Ciarlet and J.-L. Lions Eds., North Holland (1991) 17–352. [Google Scholar]
  10. P. Coorevits, P. Hild and J.-P. Pelle, A posteriori error estimation for unilateral contact with matching and nonmatching meshes. Comput. Methods Appl. Mech. Engrg. 186 (2000) 65–83. [CrossRef] [MathSciNet] [Google Scholar]
  11. P. Coorevits, P. Hild and M. Hjiaj, A posteriori error control of finite element approximations for Coulomb's frictional contact. SIAM J. Sci. Comput. 23 (2001) 976–999. [CrossRef] [MathSciNet] [Google Scholar]
  12. P. Coorevits, P. Hild, K. Lhalouani and T. Sassi, Mixed finite element methods for unilateral problems: convergence analysis and numerical studies. Math. Comp. 71 (2002) 1–25. [Google Scholar]
  13. G. Duvaut and J.-L. Lions, Les inéquations en mécanique et en physique. Dunod (1972). [Google Scholar]
  14. C. Eck and W. Wendland, A residual-based error estimator for BEM-discretizations of contact problems. Numer. Math. 95 (2003) 253–282. [CrossRef] [MathSciNet] [Google Scholar]
  15. G. Fichera, Problemi elastici con vincoli unilaterali il problema di Signorini con ambigue condizioni al contorno. Mem. Accad. Naz. Lincei. 8 (1964) 91–140. [Google Scholar]
  16. G. Fichera, Existence theorems in elasticity, in Handbuch der Physik, Band VIa/2, Springer (1972) 347–389. [Google Scholar]
  17. R. Glowinski, Lectures on numerical methods for nonlinear variational problems, in Lectures on Mathematics and Physics 65, Notes by M. G. Vijayasundaram and M. Adimurthi, Tata Institute of Fundamental Research, Bombay; Springer-Verlag, Berlin-New York (1980). [Google Scholar]
  18. W. Han and M. Sofonea, Quasistatic contact problems in viscoelasticity and viscoplasticity. American Mathematical Society (2002). [Google Scholar]
  19. J. Haslinger, I. Hlaváček and J. Nečas, Numerical methods for unilateral problems in solid mechanics, in Handbook of Numerical Analysis, Volume IV, Part 2, P.G. Ciarlet and J.-L. Lions Eds., North Holland (1996) 313–485. [Google Scholar]
  20. P. Hild, A priori error analysis of a sign preserving mixed finite element method for contact problems. Preprint 2006/33 of the Laboratoire de Mathématiques de Besançon, submitted. [Google Scholar]
  21. P. Hild and S. Nicaise, A posteriori error estimations of residual type for Signorini's problem. Numer. Math. 101 (2005) 523–549. [CrossRef] [MathSciNet] [Google Scholar]
  22. J.-B. Hiriart-Urruty and C. Lemaréchal, Convex analysis and minimization algorithms I. Springer (1993). [Google Scholar]
  23. S. Hüeber and B. Wohlmuth, An optimal error estimate for nonlinear contact problems. SIAM J. Numer. Anal. 43 (2005) 156–173. [CrossRef] [MathSciNet] [Google Scholar]
  24. N. Kikuchi and J.T. Oden, Contact problems in elasticity. SIAM (1988). [Google Scholar]
  25. T. Laursen, Computational contact and impact mechanics. Springer (2002). [Google Scholar]
  26. C.Y. Lee and J.T. Oden, A posteriori error estimation of h-p finite element approximations of frictional contact problems. Comput. Methods Appl. Mech. Engrg. 113 (1994) 11–45. [CrossRef] [MathSciNet] [Google Scholar]
  27. A. Veeser, Efficient and reliable a posteriori error estimators for elliptic obstacle problems. SIAM J. Numer. Anal. 39 (2001) 146–167. [CrossRef] [MathSciNet] [Google Scholar]
  28. R. Verfürth, A review of a posteriori error estimation and adaptive mesh-refinement techniques. Wiley and Teubner (1996). [Google Scholar]
  29. R. Verfürth, A review of a posteriori error estimation techniques for elasticity problems. Comput. Methods Appl. Mech. Engrg. 176 (1999) 419–440. [CrossRef] [MathSciNet] [Google Scholar]
  30. P. Wriggers, Computational Contact Mechanics. Wiley (2002). [Google Scholar]
  31. P. Wriggers and O. Scherf, Different a posteriori error estimators and indicators for contact problems. Mathl. Comput. Modelling 28 (1998) 437–447. [CrossRef] [Google Scholar]

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