Adaptive finite elements for elastic bodies in contact

SIAM Journal of Scientific Computing

Volumn 20, Issue 5, 1999, Pages 1605-1626

  Carstensen, C ^a   Scherf, O ^b   Wriggers, P ^b  

^a UNIVERSITY OF KIEL   (Germany)

^b LEIBNIZ UNIVERSITY HANNOVER   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ADAPTIVE ALGORITHMS; COMPUTER SIMULATION; ERROR ANALYSIS; MATHEMATICAL MODELS; NUMERICAL METHODS; VECTORS;

CONTACT OF BODIES; PENALTY METHOD; REGULARIZATION; VARIATIONAL INEQUALITY;

FINITE ELEMENT METHOD;

EID: 0033295419     PISSN: 10648275     EISSN: None     Source Type: None    
DOI: 10.1137/S1064827595295350     Document Type: Article

References (25)

1. I. BABUSKA AND A. MILLER, A feedback finite element method with a posteriori error estimation: Part I. The finite element method and some basic properties of the a posteriori error estimation, Comput. Methods Appl. Mech. Engrg., 61 (1987), pp. 1-40.
2. I. BABUSKA AND W. RHEINBOLDT, Error estimates for adaptive finite element computations, SIAM J. Numer. Anal., 15 (1978), pp. 736-754.
3. R. E. BANK, PLTMG: A Software Package for Solving Elliptic Partial Differential Equations. Users' Guide 6.0, SIAM, Philadelphia, PA, 1990.
4. P. BOIERI, F. GASTALDI, AND D. KINDERLEHRER, Existence, uniqueness, and regularity results for the two-body contact problem, Appl. Math. Optim., 15 (1987), pp. 251-277.
5. P. G. CIARLET, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978.
6. P. CLEMENT, Approximation by finite element functions using local regularization, RAIRO Sér. Rouge Anal. Numér., 9 (1975), pp. 77-84.
7. A. CURNIER AND P. ALART, A generalized Newton method for contact problems with friction, J. Méc. Théor. Appl., Spec. Issue: Numerical Methods in Mechanics of Contact Involving Friction, 7 (1988), suppl. 1, pp. 67-82.
8. K. ERIKSSON, D. ESTEP, P. HANSBO, AND C. JOHNSON, Introduction to adaptive methods for differential equations, Acta Numerica, 1995, pp. 105-158.
9. I. HLAVÁČEK, J. HASLINGER, J. NEČAS, AND J. LOVÍŠEK, Solution of Variational Inequalities in Mechanics, Springer, New York, 1988.
10. C. JOHNSON, Numerical Solutions of Partial Differential Equations by the Finite Element Method, Cambridge Press, New York, 1987.
11. C. JOHNSON, Adaptive finite element methods for the obstacle problem, Math. Models Methods Appl. Sci., 2 (1992), pp. 483-487.
12. C. JOHNSON AND P. HANSBO, Adaptive finite element methods in computational mechanics, Comput. Methods Appl. Mech. Engrg., 101 (1992), pp. 143-181.
13. N. KIKUCHI AND J. T. ODEN, Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods, SIAM, Philadelphia, PA, 1988.
14. C. Y. LEE, J. T. ODEN, AND M. AINSWORTH, Local a posteriori error estimates and numerical results for contact problems and problems of flow trough porous media, in Nonlinear Computational Mechanics, P. Wriggers and P. Wagner, eds., Springer, Berlin, 1991, pp. 671-689.
15. D. G. LUENBERGER, Linear and nonlinear programming, Addison-Wesley, Reading, MA, 1989.
16. J. PERAIRE, M. VAHDATI, K. MORGAN, AND O. C. ZIENKIEWICZ, Adaptive meshing for compressible flow computations, J. Comput. Phys., 72 (1987), pp. 449-466.
17. R. SCHOLZ, Numerical solution of the obstacle problem by the penalty method, Computing, 32 (1984), pp. 297-306.
18. S. W. SLOAN, A fast algorithm for constructing delaunay triangularization in the plane, Adv. Engrg. Software, 9 (1987), pp. 34-55.
19. R. VERFÜRTH, A posteriori error estimates for non-linear problems. Finite element discretization of elliptic equations. Math. Comp., 62 (1994), pp. 445-475.
20. R. VERFÜRTH, A Review of A Posteriori Error Estimation and Adaptive Mesh-refinement Techniques, Wiley-Teubner, Chichester, Stuttgart, 1996.
21. P. WRIGGERS AND C. MIEHE, Contact constraints within coupled thermomechanical analysis -A finite element model, Comput. Methods Appl. Mech. Engrg., 113 (1994), pp. 301-319.
22. O. C. ZIENKIEWICZ AND R. L. TAYLOR, The Finite Element Method, 4th ed., Vol. I, McGraw Hill, London, 1988.
23. O. C. ZIENKIEWICZ, Y. C. LIU, AND G. C. HUANG, Error estimation and adaptivity in flow formulation for forming problems, Internat. J. Numer. Methods Engrg., 25 (1988), pp. 23-42.
24. O. C. ZIENKIEWICZ AND J. Z. ZHU, A simple error estimator and adaptive procedure for practical engineering analysis, Internat. J. Numer. Methods Engrg., 24 (1987), pp. 337-357.
25. O. C. ZIENKIEWICZ AND J. Z. ZHU, The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique, Internat. J. Numer. Methods Engrg., 33 (1992), pp. 1331-1364.