A-posteriori modeling error estimation for hierarchic plate models

Numerische Mathematik

Volumn 74, Issue 2, 1996, Pages 221-259

  Schwab, C ^a,b  

^a ETH ZURICH   (Switzerland)

^b UNIVERSITY OF MARYLAND BALTIMORE COUNTY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030521479     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110050215     Document Type: Article

References (28)

1. Actis, R.L. (1991): Hierarchic Models for Laminated Plates. Doctoral Dissertation Washington University, St. Louis, Mo
2. Antman, S.S., Marlow R.S. (1991): Material Constraints, Lagrange Multipliers, and Compatibility. Applications to Rod and Shell Theories, Arch. Rat. Mech. Anal. 116, 257-299
3. Babuška, I, Li L. (1991): Hierarchic Modelling of Plates. Computers and Structures 40, 419-430
4. Babuška, I., Lee I., Schwab C. (1994): On the a-posteriori estimation of the modeling error for the heat conduction in a plate and its use for adaptive hierarchical modeling. Appl. Num. Math. 14, 5-21
5. Babuška, I., Szabo, B.A., Actis R. (1992): Hierarchic Models for Laminated Composites. Int. Journ. Num. Meth. Eng. 33, 503-536
6. Babuška, I., Schwab, C., A-posteriori error estimation for hierarchic models of elliptic boundary value problems on thin domains. SIAM J. Num. Anal (in press)
7. Ciarlet, P.G. (1990): Plates and junctions in elastic multistructures - an asymptotic analysis. Masson Publishers, Paris and Springer-Verlag, Berlin Heidelberg New York
8. Destuynder, P. (1981): Comparaison entre les modè les tridimensionnels et bidimensionnels de plaques en élasticité, RAIRO Anal. Numérique 15, 331-369
9. Germain, S., (1821) Entry submitted to the first class of the French Academy in 1816, published as Reserches sur la théorie des surfaces élastiques, Mme. V. Courcier, Paris
10. Kirchhoff, B. (1850): Über das Gleichgewicht und die Bewegung einer elastischen Scheibe, Journ. Reine Angew. Math. 40, 51-58
11. Miara, B. (1989): Optimal spectral approximation in linearized plate theory. Applicable Analysis 31, 291-307
12. Mindlin, R.D. (1951): Influence of rotatory inertia and shear on flexural motion of isotropic elastic plates. J. Appl. Mech. 18, 31-38
13. Nečas, J. (1967): Les Me thodes Directes en Théorie des Equations Elliptiques. Masson, Paris
14. Oleinik, O.A., Shamaev, A.S., Yosifian, G.A. (1992): Mathemat cal Problems in Elasticity and Homogenization. Studies in Mathematics and its Applications Vol. 26, North-Holland Publ. Amsterdam, New York
15. Reissner, E. (1945): The effect of transverse shear deformation on the bending of elastic plates. J. Appl. Mech. 67, A69-A77
16. Reissner, E. (1947): On bending of elastic plates. Quart. Appl. Math. 5, 55-68
17. Schwab, C. (1989): Dimensional reduction for elliptic boundary value problems. Ph.D. thesis Dept. of Mathematics, Univ. of Maryland College Park, MD 20742 USA,
18. Schwab, C. (1994): Boundary Layer Resolution in Hierarchical Models of laminated composites R.A.I.R.O. Anal. Numér., Sér. rouge 28, 517-537
19. Schwab, C. (1993): A-posteriori error estimation for hierarchic plate models. In: Proc. EUROMECH 302 conference, Paris May (E. Sanchez-Palencia, Ed.)
20. Schwab, C. (1995): Habilitation thesis Stuttgart University, Germany
21. Schwab, C., Babuška, I. (1994): Subspace correction methods for the iterative solution of hierarchic plate models 1. Technical Note BN-1169, Inst. Phys. Science & Technology, Univ. Maryland College Park. To appear in Comp. Meth. Appl. Mech. Engg.
22. Schwab, C., Suri, M. (1995): The p and hp versions of the finite element method for problems with boundary layers. Math. Research Report 95-01, Department of Mathematics, UMBC, February. Math. Comp.
23. Schwab, C., Suri, M. (1994): Locking and boundary layer effects in the finite element approximation of the Reissner-Mindlin plate model, AMS Proc. Symp. Appl. Math. 48, 367-371,
24. Schwab, C., Wright S. (1992): Boundary Layers of Hierarchical Beam-and Plate Models. Research Report 92-08, Dept. of Mathematics, Univ. of Maryland, Baltimore County, Baltimore, MD 21228-5398, May (in press in J. Elasticity)
25. Stein, E.M. (1970): Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton, NJ,
26. Suri, M., Babuška, I., Schwab, C. (1995): Locking effects in the finite element approximation of plate models. Mathematics of Computation 64, 461-482
27. Szabo, B.A, Actis R.L. (1992): Hierarchic Models for Laminated Plates. In: Adaptive, Multilevel and Hierarchical Computational Strategies, A.K. Noor (ed.), AMD-Vol. 157, ASME NY, 69-94
28. Szabo, B.A., Sahrmann G.J. (1988): Hierarchic Plate and Shell Models Based on p-Extension. Int. J. Num. Meth. Engg. 26, 1855-1881