A posteriori error estimation for hierarchic models of elliptic boundary value problems on thin domains

SIAM Journal on Numerical Analysis

Volumn 33, Issue 1, 1996, Pages 221-246

  Babuska I ^a   Schwab, C ^b  

^a UNIVERSITY OF MARYLAND   (United States)

^b ETH ZURICH   (Switzerland)

Author keywords

A posteriori error estimation; Hierarchic modeling; Plates

Indexed keywords

EID: 0000024773     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/0733013     Document Type: Article

References (12)

1. S. GERMAIN, Reserches sur la théorie des surfaces élastiques, Mme. V. Courcier, Paris 1821.
2. G. KIRCHHOFF, Über das Gleichgewicht und die Biegung einer elastischen Scheibe, J. Reine Angew. Math., 40 (1850), pp. 51-58.
3. A. K. NOOR AND S. W. BURTON, Assessment of shear deformation theories for multilayered composite plates, Appl. Mech. Rev., 42 (1989), pp. 1-12.
4. W. GILEWESKI AND M. RADWONSKA, A survey of finite element models for the analysis of moderately thick shells, Finite Elem. Anal. Des., 9 (1991), pp. 1-21.
5. P. G. CIARLET, Plates and Junctions in Elastic Multi-Structures: An Asymptotic Analysis, Masson, Paris and Springer-Verlag, Berlin, 1990.
6. D. MORGENSTERN, Herleitung der Plattentheorie aus der dreidimensionalen Elastizitätstheorie, Arch. Rational Mech. Anal., 4 (1959), pp. 145-152.
7. I. BABUŠKA AND T. PITKÄRANTA, The plate paradox for hard and soft simple support, SIAM J. Math. Anal., 21 (1990), pp. 551-576.
8. I. BABUSKA, I. LEE, AND C. SCHWAB, On the A-Posteriori Estimation of the Modelling Error for the Heat Conduction in a Plate and its Use for Adaptive Hierarchic Modelling, Tech. Note BN-1145, Institute for Physical Science and Technology, University of Maryland, College Park, MD, 1993.
9. M. VOGELIUS AND I. BABUŠKA, On a dimensional reduction method I. The optimal selection of basis functions, Math. Comp., 37 (1981), pp. 31-46.
10. C. SCHWAB, Boundary layer resolution in hierarchic plate modelling, RAIRO Model. Math. Anal. Numer., 28 (1994), pp. 517-537.
11. J. L. LIONS AND M. MAGENES, Non Homogeneous Boundary Value Problems and Applications, Vol. II, Springer-Verlag, Berlin, New York, 1982.
12. M. H. PROTTER AND H. F. WEINBERGER, Maximum Principles in Differential Equations, 2nd ed., Springer-Verlag, Berlin, New York, 1984.