Free Access
| Issue |
ESAIM: M2AN
Volume 41, Number 5, September-October 2007
|
|
|---|---|---|
| Page(s) | 897 - 923 | |
| DOI | https://doi.org/10.1051/m2an:2007045 | |
| Published online | 23 October 2007 | |
- R.A. Adams, Sobolev spaces. Academic Press (1975). [Google Scholar]
- 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]
- 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]
- F. Ben Belgacem and Y. Renard, Hybrid finite element methods for the Signorini problem. Math. Comp. 72 (2003) 1117–1145. [CrossRef] [MathSciNet] [Google Scholar]
- 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]
- D. Braess, A posteriori error estimators for obstacle problems - another look. Numer. Math. 101 (2005) 415–421. [CrossRef] [MathSciNet] [Google Scholar]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- G. Duvaut and J.-L. Lions, Les inéquations en mécanique et en physique. Dunod (1972). [Google Scholar]
- 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]
- 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]
- G. Fichera, Existence theorems in elasticity, in Handbuch der Physik, Band VIa/2, Springer (1972) 347–389. [Google Scholar]
- 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]
- W. Han and M. Sofonea, Quasistatic contact problems in viscoelasticity and viscoplasticity. American Mathematical Society (2002). [Google Scholar]
- 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]
- 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]
- 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]
- J.-B. Hiriart-Urruty and C. Lemaréchal, Convex analysis and minimization algorithms I. Springer (1993). [Google Scholar]
- 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]
- N. Kikuchi and J.T. Oden, Contact problems in elasticity. SIAM (1988). [Google Scholar]
- T. Laursen, Computational contact and impact mechanics. Springer (2002). [Google Scholar]
- 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]
- 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]
- R. Verfürth, A review of a posteriori error estimation and adaptive mesh-refinement techniques. Wiley and Teubner (1996). [Google Scholar]
- 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]
- P. Wriggers, Computational Contact Mechanics. Wiley (2002). [Google Scholar]
- 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]
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.