A family of Discontinuous Galerkin finite elements for the Reissner-Mindlin plate

Journal of Scientific Computing

Volumn 22-23, Issue , 2005, Pages 25-45

  Arnold, Douglas N ^a   Brezzi, Franco ^b   Marini, L Donatella ^b  

^a UNIVERSITY OF MINNESOTA   (United States)

^b UNIVERSITY OF PAVIA   (Italy)

Author keywords

Discontinuous Galerkin; Locking free finite elements; Reissner Mindlin plates

Indexed keywords

COMPUTATIONAL COMPLEXITY; ERROR ANALYSIS; ESTIMATION; FINITE ELEMENT METHOD; INTERPOLATION; PROBLEM SOLVING;

DISCONTINUOUS GALERKIN METHOD; LOCKING-FREE FINITE ELEMENTS; REISSNER-MINDLIN PLATES; SOBOLEV SPACES;

GALERKIN METHODS;

EID: 17444422862     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10915-004-4134-8     Document Type: Article

References (27)

1. Agmon, S. (1965). Lectures on Elliptic Boundary Value Problems, Van Nostrand Mathematical Studies, Princeton, NJ.
2. Arnold, D. N. (1982). An interior penalty finite element method with discontinuous elements. SIAM J. Numer. Anal. 19, 742-760.
3. Arnold, D. N., Brezzi, F., Cockburn, B., and Marini, L. D. (2000). Discontinuous Galerkin methods for elliptic problems. In Discontinuous Galerkin Methods (Newport, RI, 1999), Lecture Notes Computational Science Engineering Vol. 11, Springer, Berlin, pp. 89-101.
4. Arnold, D. N., Brezzi, F., Cockburn, B., and Marini, L. D. (2002). Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39, 1749-1779.
5. Arnold, D. N., and Falk, R. S. (1989). A uniformly accurate finite element method for the Reissner-Mindlin plate. SIAM J. Numer. Anal. 26, 1276-1290.
6. Auricchio, F., and Lovadina, C. (1999). Partial selective reduced integration schemes and kinematically linked interpolations for plate bending problems. Math. Models Meth. Appl. Sci. 9, 693-722.
7. Auricchio, F., and Lovadina, C. (2001). Analysis of kinematic linked interpolation methods for Reissner-Mindlin plate problems. Comput. Meth. Appl. Mech. Eng. 190, 18-19.
8. Auricchio, F., and Taylor, R. L. (1994). A shear deformable plate element with an exact thin limit. Comput. Meth. Appl. Mech. Eng. 118, 393-412.
9. Bathe, K. J. (1994). Finite Element Procedures, Prentice-Hall, Englewood Cliffs, NJ.
10. 1 functions. SIAM J. Numer. Anal. 41, 306-324.
11. 1 vector fields. Math. Comput. 73, 1067-1087.
12. Brezzi, F., Bathe, K. J., and Fortin, M. (1989). Mixed-interpolated elements for Reissner-Mindlin plates. Int. J. Numer. Meth. Eng. 28, 1787-1801.
13. Brezzi, F., Douglas, J. Jr., and Marini, L. D. (1985). Two families of mixed finite elements for second order elliptic problems. Numer. Math. 47, 217-235.
14. Brezzi, F., and Fortin, M. (1999). Mixed and Hybrid Finite Element Methods, Springer, New York.
15. Brezzi, F., Fortin, M., and Stenberg, R. (1991). Error analysis of mixed-interpolated elements for Reissner-Mindlin plates. Math. Models Meth. Appl. Sci. 1, 125-151.
16. Brezzi, F., and Marini, L. D. (2003). A nonconforming element for the Reissner-Mindlin plate. Comput. Struct. 81, 515-522.
17. Bucalem, M. L., and Bathe, K. J. (1997). Finite element analysis of shell structures. Arch. Comput. Meth. Eng. 4, 3-61.
18. Bucalem, M. L., and Bathe, K. J. (1993). Higher-order MITC general shell elements. Int. J. Numer. Meth. Eng. 36, 3729-3754.
19. Chapelle, D., and Bathe, K. J. (1998). Fundamental considerations for the finite element analysis of shell structures. Comput. Struct. 66, 19-36.
20. Chapelle, D., and R. Stenberg, R. (1999). Stabilized finite element formulations for shells in a bending dominated state. SIAM J. Numer. Anal. 36, 32-73.
21. Duran, R., and Liberman, E. (1992). On mixed finite-element methods for the Reissner-Mindlin plate model. Math. Comput. 58, 561-573.
22. Flores, F. G., Oñate, E., and Zaráte, F. (1995). New assumed strain triangles for nonlinear shell analysis. Comput. Mech. 17, 107-114.
23. Hansbo, P., and Larson, M. G. (2000). Discontinuous Galerkin and the Crouzeix-Raviart element: Application to Elasticity, Chalmers Finite Element Center Preprint 2000-9, Chalmers University of Technology, Sweden.
24. Hughes, T. J. R. (1987). The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, Englewood Cliffs, NJ.
25. Lovadina, C. (1996). A new class of mixed finite element methods for Reissner-Mindlin plates. SIAM J. Numer. Anal 33, 2457-2467.
26. Lovadina, C. (1998). Analysis of a mixed finite element method for the Reissner-Mindlin plate problems. Comput. Meth. Appl. Mech. Eng. 163, 71-85.
27. 1 element for Reissner-Mindlin plate. Math. Models Meth. Appl. Sci. 11, 1311-1342.