A posteriori error estimation for unilateral contact with matching and non-matching meshes

Computer Methods in Applied Mechanics and Engineering

Volumn 186, Issue 1, 2000, Pages 65-83

  Coorevits, Patrice ^a   Hild, Patrick ^b   Pelle, Jean Pierre ^a  

^a Grande Voie des Vignes   (France)

^b UNIVERSITÉ DE SAVOIE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; ELASTICITY; ERROR ANALYSIS; PROBLEM SOLVING; STRESS ANALYSIS;

UNILATERAL CONTACT PROBLEMS;

FINITE ELEMENT METHOD;

EID: 0033738265     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(99)00105-X     Document Type: Article

References (19)

1. G. Duvaut, J.-L. Lions, Les inéquations en mécanique et en physique, Dunod, 1972.
2. G. Fichera, in: S. Flugge (Ed.), Encyclopedia of Physics, vol. VIa/2, Springer, Berlin, 1972, pp. 391-424.
3. N. Kikuchi, J.T. Oden, Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods, SIAM, Philadelphia, 1988.
4. J. Haslinger, I. Hlavacek, J. Necas, Numerical methods for unilateral problems in solid mechanics, in: P.G. Ciarlet, J.L. Lions (Eds.), Handbook of Numerical Analysis, vol. IV, Part 2, North Holland, 1996.
5. Ben Belgacem F., Hild P., Laborde P. The mortar finite element method for contact problems. Math. Comput. Modelling. 28:1998;263-271.
6. Ben Belgacem F., Hild P., Laborde P. Approximation of the unilateral contact problem by the mortar finite element method. C.R. Acad. Sci. Paris, Série I. 324:1997;123-127.
7. F. Ben Belgacem, P. Hild, P. Laborde, Extension of the mortar finite element method to a variational inequality modelling unilateral contact, Math. Modelling Meth. in Appl. Sci., vol. 9, 1999.
8. P. Hild, Problèmes de contact unilatéral et maillages éléments finis incompatibles, Thèse de l'Université Paul Sabatier, Toulouse 3, 1998.
9. Babuska I., Rheinboldt W.C. Error estimates for adaptive finite element computation. Siam. J. Num. Anal. 15:1978;736-754.
10. Zienkiewicz O.C., Zhu J.Z. A simple error estimator and adaptive procedure for practical engineering analysis. Internat. J. Num. Meth. Engrg. 24:1987;337-357.
11. P. Ladevèze, G. Coffignal, J.P. Pelle, Accuracy of elastoplastic and dynamic analysis, Accuracy estimates and adaptative refinements, in: Babuska, Gago, Oliveira, Zienkiewicz (Eds.), Finite Element Computations, Wiley, New York, 1986, pp. 181-203.
12. Ladevèze P., Pelle J.P., Rougeot P. Error estimates and mesh optimization for finite element computation. Engrg. Comp. 8:1991;69-80.
13. P. Wriggers, O. Scherf, C. Carstensen, Adaptive techniques for the contact of elastic bodies in: Hughes, Onate, Zienkiewicz (Eds.), Recent Developments in Finite Element Analysis, CIMNE, 1994, pp. 78-86.
14. P. Ladevèze, Nonlinear computational structural mechanics, New Approaches and Non-incremental Methods of Calculation, Springer, Berlin, 1998.
15. Prager W., Synge J.L. Approximations in elasticity based on the concept of function space. Quart. Appl. Math. 5:1947;261-269.
16. Ekeland I., Temam R. Convex Anal. Variational Problems. 1976;Amsterdam, North-Holland.
17. P. Coorevits, J.P. Dumeau, J.P. Pelle, Control of analysis with isoparametric elements in 2D and in 3D, submitted.
18. Coorevits P., Ladevèze P., Pelle J.P. Mesh optimization for problems with steep gradients. Engrg. Comp. 11:1994;129-144.
19. Coorevits P., Ladevèze P., Pelle J.P. An automatic procedure for finite element analysis in 2D elasticity. Comp. Meth. Appl. Mech. Engrg. 121:1995;91-120.