Analytical and computational assessment of locking in the hp finite element method

Computer Methods in Applied Mechanics and Engineering

Volumn 133, Issue 3-4, 1996, Pages 347-371

  Suri, Manil ^a  

^a UNIVERSITY OF MARYLAND BALTIMORE COUNTY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; NUMERICAL METHODS; PROBLEM SOLVING;

CURVED ELEMENTS; LIMITING VALUE; MIXED METHODS; NUMERICAL LOCKING; PARAMETER DEPENDENT PROBLEMS;

FINITE ELEMENT METHOD;

EID: 0030191620     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/0045-7825(95)00947-7     Document Type: Article

References (25)

1. D.N. Arnold, Discretization by finite elements of a model parameter dependent problem, Numer. Math. 37 (1981) 405-421.
2. I. Babuška and A.K. Aziz, On the angle condition in the finite element method, SIAM J. Numer. Anal. 13 (1976) 214-226.
3. I. Babuška and L. Li, The problem of plate modeling: Theoretical and computational results, Comput. Methods Appl. Mech. Engrg. 100 (1992) 249-273.
4. I. Babuška and M. Suri, The p and h-p versions of the finite element method, an overview, Comput. Methods Appl. Mech. Engrg. 80 (1990) 5-26.
5. I. Babuška and M. Suri, On the locking and robustness in the finite element method, SIAM J. Numer. Anal. 29 (1992) 1261-1293.
6. I. Babuška and M. Suri, Locking effects in the finite element approximation of elasticity problems, Numer. Math. 62 (1992) 439-463.
7. I. Babuška and B.A. Szabo, Rates of convergence of the finite element method, Int. J. Numer. Methods Engrg. 18 (1982) 323-341.
8. M. Bernardi and Y. Maday, Approximations Spectrales de Problemes aux Limites Elliptiques (Springer-Verlag, New York, 1992).
9. F. Brezzi and K.J. Bathe, Studies of finite element procedures - the inf-sup condition, equivalent forms and applications, in: K.J. Bathe and D.R.J. Owen, eds., Reliability of Methods for Engineering Analysis (Pineridge Press, Swansea, 1986) 1787-1801.
10. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods (Springer, Berlin, 1991).
11. P.G. Ciarlet, The Finite Element Method for Elliptic Problems (North-Holland, Amsterdam, 1978).
12. L. Li, Discretization of the Timoshenko beam problem by the p and the h-p versions of the finite element method, Numer. Math. 57 (1990) 1-8.
13. R.H. MacNeal, Finite Elements: Their Design and Performance (Marcel Dekker, Inc., New York, 1994).
14. N-2 method for the approximation of the Stokes problem, Technical report, 1992.
15. N.I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity (Noordhoff, Groningen, The Netherlands, 1953).
16. J. Pitkäranta, The problem of membrane locking in finite element analysis of cylindrical shells, Numer. Math. 61 (1992) 523-542.
17. L.R. Scott and M. Vogelius, Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials, RAIRO Math. Modeling Numer. Anal. 19 (1985) 111-143.
18. C. Schwab and M. Suri, Locking and boundary layer effects in the finite element approximation of the Reissner-Mindlin plate model, AMS Proc. of Symposia in Applied Mathematics 48 (1994) 367-371.
19. R. Stenberg and M. Suri, Mixed hp finite element methods for problems in elasticity and Stokes flow, Numer. Math. 72 (1996) 367-390.
20. R. Stenberg and M. Suri, An hp error analysis of MITC plate elements, SIAM J. Numer. Anal., in preparation.
21. M. Suri, A reduced constraint hp finite element method for shell problems, Math. Comput., in preparation.
22. M. Suri, I. Babuška and C. Schwab, Locking effects in the finite element approxmation of plate models. Math. Comput. 64 (1995) 461-482.
23. B.A. Szabo and I. Babuška, Finite Element Analysis (Wiley, New York, 1991).
24. M. Vogelius, An analysis of the p-version of the finite element method for nearly incompressible materials. Uniformly valid, optimal error estimates, Numer. Math. 41 (1983) 19-37.
25. Z. Zhang, Locking and robustness in the finite element method for circular arch problems, Numer. Math. 69 (1995) 509-522.