An adaptive finite element discretisation for a simplified Signorini problem

Calcolo

Volumn 37, Issue 2, 2000, Pages 65-77

  Blum, H ^a   Suttmeier, E T ^a  

^a TU DORTMUND UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ERROR ANALYSIS;

ADAPTIVE FINITE ELEMENT; ADAPTIVE MESHES; ERROR ESTIMATORS; FINITE-ELEMENT DISCRETIZATION; MESH DESIGNS; POSTERIORI ERROR CONTROL; POSTERIORI ESTIMATES; SIGNORINI PROBLEM; VARIATIONAL INEQUALITIES; VARIATIONAL PROBLEMS;

VARIATIONAL TECHNIQUES;

EID: 0001908752     PISSN: 00080624     EISSN: None     Source Type: Journal    
DOI: 10.1007/s100920070008     Document Type: Article

References (22)

1. Becker, R., Kanschat, G., Suttmeier, F.-T.: DEAL - differential equations analysis library. Available via http://gaia.iwr.uni-heidelberg.de/DEAL.html, 1995
2. Becker, R., Rannacher, R.: A feed-back approach to error control in finite element methods: Basic analysis and examples. East-West J. Numer. Math. 4, 237-264 (1996)
3. Brézis, H.: Problèmes unilatéraux. (Thèse.) J. Math. Pures Appl. (9) 51, 1-168 (1972)
4. Brezzi, F., Hager, W.W., Raviart, P.-A.: Error Estimates for the finite element solution of variational inequalities. I. primal theory. Numer. Math. 28, 431-443 (1977)
5. Carstensen, C., Scherf, O., Wriggers, P.: Adaptive finite elements for elastic bodies in contact. SIAM J. Sci. Comput 20, 1605-1626 (1999)
6. Dobrowolski, M., Staib, T.: On finite element approximation of a second order unilateral variational inequality. Numer. Funct. Anal. Optim. 13, 243-247 (1992)
7. Falk, R.S.: Error estimates for the approximation of a class of variational inequalities. Math. Comp. 28, 963-971 (1974)
8. Glowinski, R.: Numerical methods for nonlinear variational problems. (Springer Series in Computational Physics) New York: Springer 1983
9. Glowinski, R., Lions, J.-L., Trémolières, R.: Numerical analysis of variational inequalities. Amsterdam: North-Holland 1981
10. Kanschat, G.: Parallel and adaptive Galerkin methods for radiative transfer problems. Dissertation. Heidelberg: Univ. Heidelberg, Naturwiss.-Math. Gesamtfax. 1996
11. Kikuchi, N., Oden, J.T.: Contact problems in elasticity: a study of variational inequalities and finite element methods. (SIAM Studies in Applied Mathematics 8) Philadelphia: SIAM 1988
12. Kinderlehrer, D., Stampacchia, G.: An introduction to variational inequalities and their applications. New York: Academic Press 1980
13. Kornhuber, R.: A posteriori error estimates for elliptic variational inequalities. Comput. Math. Applic. 31, 49-60 (1996)
14. Lions, J.-L., Stampacchia, G.: Variational inequalities. Comm. Pure Appl. Math. 20, 493-519 (1967)
15. Mosco, U.: Error estimates for some variational inequalities. In: Galligani, I., Magenes, E. (eds.) Mathematical aspects of finite element methods, (Lecture Notes in Math. 606) Berlin: Springer 1977, pp. 224-236
16. ∞-convergence of finite element approximations. In: Galligani, I., Magenes, E. (eds.) Mathematical aspects of finite element methods, (Lecture Notes in Math. 606) Berlin: Springer 1977, pp. 261-274
17. 2-Konvergenz finiter Elemente bei Variationsungleichungen. Bonn. Math. Schrift 89, 1-12 (1976)
18. Rannacher, R., Suttmeier, F.-T.: A feed-back approach to error control in finite element methods: application to linear elasticity. Comput. Mech. 19, 434-446 (1997)
19. Rannacher, R., Suttmeier, F.-T.: A posteriori error control in finite element methods via duality techniques: application to perfect plasticity. Comput. Mech. 21, 123-133 (1998)
20. F.-T. Suttmeier: Adaptive finite element approximation of problems in elasto-plasticity theory. Dissertation. Heidelberg: Univ. Heidelberg, Naturwiss.-Math. Gesamtfax. 1997
21. Verfürth, R.: A review of a posteriori error estimation and adaptive mesh-refinement techniques. (Wiley-Teubner Skripten zur Numerik). Stuttgart: Teubner 1996
22. Zienkiewicz, O.C., Zhu, J.Z.: A simple error estimator and adaptive procedure for practical engineering analysis. Internat. J. Numer. Methods Engrg. 24, 337-357 (1987)