On the ellipticity condition for model-parameter dependent mixed formulations

Computers and Structures

Volumn 88, Issue 9-10, 2010, Pages 581-587

  Chapelle, Dominique ^a   Bathe, Klaus Jürgen ^b  

^a INRIA   (France)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Coercivity; Finite element; Inf sup; Mixed method; Small parameter dependence

Indexed keywords

COERCIVITIES; DISCRETE PROBLEMS; FINITE ELEMENT; FINITE-ELEMENT DISCRETIZATION; INF-SUP CONDITIONS; LIMIT PROBLEM; MIXED FORMULATIONS; MIXED METHOD; MODEL PARAMETERS; NUMERICAL TESTS; PARAMETER DEPENDENCE; PLATES AND SHELLS;

COERCIVE FORCE;

FINITE ELEMENT METHOD;

EID: 77950519446     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruc.2010.01.009     Document Type: Article

References (23)

1. Bathe K.J. The finite element method. In: Wah B. (Ed). Encyclopedia of computer science and engineering (2009), John Wiley & Sons 1253-1264
2. Bathe K.J. Finite element procedures (1996), Prentice Hall, Englewood Cliffs
3. Brezzi F., and Fortin M. Mixed and hybrid finite element methods (1991), Springer-Verlag, New York
4. Chapelle D., and Bathe K.J. The finite element analysis of shells - fundamentals (2003), Springer-Verlag
5. Chapelle D., and Bathe K.J. The finite element analysis of shells - fundamentals. 2nd ed. (2010), Springer-Verlag
6. Brezzi F., and Bathe K.J. A discourse on the stability conditions for mixed finite element formulations. Comput Methods Appl Mech Eng 82 (1990) 27-57
7. Iosilevich A., Bathe K.J., and Brezzi F. On evaluating the inf-sup condition for plate bending elements. Int J Numer Methods Eng 40 (1997) 3639-3663
8. Bathe K.J., Iosilevich A., and Chapelle D. An inf-sup test for shell finite elements. Comput Struct 75 5 (2000) 439-456
9. Bathe K.J. The inf-sup condition and its evaluation for mixed finite element methods. Comput Struct 79 (2001) 243-252 971
10. Häggblad B., and Bathe K.J. Specifications of boundary conditions for Reissner/Mindlin plate bending finite elements. Int J Numer Methods Eng 30 (1990) 981-1011
11. Lee P.S., and Bathe K.J. On the asymptotic behavior of shell structures and the evaluation in finite element solutions. Comput Struct 80 (2002) 235-255
12. Banach S. Théorie des opérations linéaires (1932), Warszawa
13. Zienkiewicz OC, Taylor RL. The finite element method, vols. 1 and 2, 4th ed. London: McGraw Hill; 1989/1991.
14. Arnold D.N., and Brezzi F. The partial selective reduced integration method and applications to shell problems. Comput Struct 64 1-4 (1997) 879-880
15. Chapelle D., and Stenberg R. An optimal low-order locking-free finite element method for Reissner-Mindlin plates. Math Models Methods Appl Sci 8 3 (1998) 407-430
16. Chapelle D., and Stenberg R. Stabilized finite element formulations for shells in a bending dominated state. SIAM J Numer Anal 36 1 (1998) 32-73
17. Glowinski R., and Le Tallec P. Augmented Lagrangian and operator-splitting methods in nonlinear mechanics. SIAM studies in applied mathematics (1989), SIAM, Philadelphia
18. Chapelle D., and Bathe K.J. The inf-sup test. Comput Struct 47 4/5 (1993) 537-545
19. Arnold D.N. Discretization by finite elements of a model parameter dependent problem. Numer Math 37 (1981) 405-421
20. Bathe K.J., Bucalem M.L., and Brezzi F. Displacement and stress convergence of our MITC plate bending elements. Eng Comput 7 December (1990) 291-302
21. Hiller J.F., and Bathe K.J. Measuring convergence of mixed finite element discretizations: an application to shell structures. Comput Struct 81 8-11 (2003) 639-654
22. Lee P.S., and Bathe K.J. Development of MITC isotropic triangular shell finite elements. Comput Struct 82 (2004) 945-962
23. Boffi D., Brezzi F., and Gastaldi L. On the convergence of eigenvalues for mixed formulations. Annali Sc Norm Sup Pisa Cl Sci 25 (1997) 131-154