Generalized Hessian and external approximations in variational problems of second order

Journal of Elasticity

Volumn 70, Issue 1-3, 2003, Pages 149-174

  Davini, Cesare ^a   Paroni, Roberto ^a  

^a UNIVERSITY OF UDINE   (Italy)

Author keywords

convergence; Anisotropic plates; Non conforming approximations; Numerical methods

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; FUNCTION EVALUATION; LAGRANGE MULTIPLIERS; MATHEMATICAL OPERATORS; NUMERICAL METHODS; PIECEWISE LINEAR TECHNIQUES; PROBLEM SOLVING; TENSORS; THEOREM PROVING; TOPOLOGY; VARIATIONAL TECHNIQUES;

ANISOTROPIC PLATES; GENERALIZED HESSIAN APPROXIMATION; HADAMARD LEMMA; SOBOLEV SPACE;

APPROXIMATION THEORY;

EID: 0042071774     PISSN: 03743535     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:ELAS.0000005534.03840.19     Document Type: Article

References (17)

1. M. Angelillo, A. Fortunato and F. Fraternali, The lumped stress method and the discrete-continuum approximation, Part I: Theory. Internat. J. Solids Struct. 39 (2002) 6211-6240.
2. M. Angelillo, A. Fortunato and F. Fraternali, The lumped stress method and the discrete-continuum approximation, part II: Applications. Ibid.
3. S. Balasundaram and P.K. Bhattacharyya, A mixed finite element method for fourth order partial differential equations. Z. angew. Math. Mech. 66 (1986) 489-499.
4. F. Brezzi, and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer, New York (1991).
5. M. Carriero, A. Leaci, and F. Tomarelli, Special bounded Hessian and elastic-plastic plate. Rend. Accad. Naz. Sci. XL Mem. Mat. 16 (1992) 223-258.
6. P.G. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1978).
7. P.G. Ciarlet, Basic error estimates for elliptic problems. In: P.G. Ciarlet and J.L. Lions (eds), Handbook of Numerical Analysis. North-Holland, Amsterdam (1991).
8. B. Dacorogna, Direct Methods in the Calculus of Variations. Springer, New York (1989).
9. G. Dal Maso, An Introduction to Γ-Convergence. Birkhäuser, Boston (1993).
10. C. Davini, Note on a parameter lumping in the vibrations of elastic beams. Rend. Ist. Matematica Università di Trieste 28 (1996) 83-99.
11. C. Davini, Γ-convergence of external approximations in boundary value problems involving the bi-Laplacian. J. Comput. Appl. Math. 140 (2002) 185-208. (2000) (to appear).
12. C. Davini and I. Pitacco, Relaxed notions of curvature and a lumped strain method for elastic plates. SIAM J. Numer. Anal. 35 (1998) 677-691.
13. C. Davini and I. Pitacco, An unconstrained mixed method for the biharmonic problem. SIAM J. Numer. Anal. 38 (2000) 820-836.
14. I. Ekeland and G. Temam, Convex Analysis and Variational Problems. North-Holland, Amsterdam (1976).
15. R. Glowinski, Approximations externes, par éléments finis de Lagrange d'ordre un et deux, du problème de Dirichlet pour l'operateur biharmonique. Méthode iterative de résolution des problèmes approaches. In: J.J.H. Miller (ed.), Topics in Numerical Analysis. Academic Press, New York (1973) 123-171.
16. N. Nataraj, P.K., Bhattacharyya, S. Balasundaram and S. Gopalsamy, On a mixed-hybrid finite element method for anisotropic plate bending problems. Internat. J. Numer. Methods Engrg. 39 (1996) 4063-4089.
17. J.E. Roberts and J.-M. Thomas, Mixed and hybrid methods. In: P.G. Ciarlet and J.L. Lions (eds), Handbook of Numerical Analysis. North-Holland, Amsterdam (1991).