The design and analysis of the Generalized Finite Element Method

Computer Methods in Applied Mechanics and Engineering

Volumn 181, Issue 1-3, 2000, Pages 43-69

  Strouboulis, T ^a   Babuska I ^b   Copps, K ^a  

^a Texas AandM University   (United States)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; INTEGRATION; PROBLEM SOLVING; STIFFNESS MATRIX;

GENERALIZED FINITE ELEMENT METHOD;

FINITE ELEMENT METHOD;

EID: 0033639850     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(99)00072-9     Document Type: Article

References (27)

1. Belytschko T., Lu Y.Y., Gu L. Element-free galerkin methods. Int. J. Numer. Meth. Engrg. 37:1994;229-256.
2. Belytschko T., Krongauz Y., Organ D., Fleming M., Krysl P. Meshless methods: An overview and recent developments. Comp. Meth. Appl. Mech. Engrg. 139:1996;3-48.
3. Duarte C.A.M., Oden J.T. hp clouds - An hp meshless method. Numer. Meth. for Partial Diff. Eqns. 12:1996;673-705.
4. J.T. Oden, C.A.M. Duarte, Solution of singular problems using hp clouds, in: J.R. Whiteman (Ed.), The Mathematics of Finite Elements and Applications, Wiley, Newyork, 1997, pp. 35-54.
5. Liu W.K., Jun S., Li S., Adee J., Belytschko T. Reproducing kernel particle methods for structural dynamics. Int. J. Numer. Meth. Engrg. 38:1995;1655-1679.
6. Babuška I., Melenk J.M. The partition of unity method. Int. J. Numer. Meth. Engrg. 40:1997;727-758.
7. Krongauz Y., Belytschko T. Enforcement of essential boundary conditions in meshless approximations using finite elements. Comput. Meth. Appl. Mech. Engrg. 131:1996;133-142.
8. Babuška I., Caloz G., Osborn J. Special finite element methods in a class of second order elliptic problems with rough coefficients. SIAM Num. Anal. 31:1994;945-981.
9. Jirousek J., Wrobleski A. T-elements: State of the art and future trends. Arch. Comput. Meth. Engrg. State of Art Rev. 3:1996;289-314.
10. V. Apanovitch, The method of external finite element approximation, Minsk, 1991 ISBN 5-339-00597-6.
11. J.M. Melenk, Finite element methods with harmonic shape functions for solving Laplace's equation, M.A. Thesis, University of Maryland, College Park, MD, 1992.
12. J.M. Melenk, On generalized finite element methods, Ph.D. Dissertation, University of Maryland, College Park, 1995 (Advisor: I. Babuška).
13. Babuška I., Melenk J.M. The partition of unity finite element method: Basic theory and applications. Comp. Meth. Appl. Mech. Engrg. 139:1996;289-314.
14. Melenk J.M., Babuška I. Approximation with harmonic and generalized harmonic polynomials in the partition of unity method. Comput. Assist. Mech. Engrg. Sci. 4:1997;607-632.
15. Oden J.T., Duarte C.A.M., Zienkiewicz O.C. A new cloud based hp finite element method. Comp. Meth. Appl. Mech. Engrg. 153:1998;117-126.
16. R.E. Bank, A.H. Sherman, A. Weiser, Refinement algorithms and data structures for regular local mesh refinement, in: R. Stepleman et al. (Ed.), Scientific Computing, IMACS/North-Holland, Amsterdam, 1983, pp. 3-17.
17. Babuška I., Miller A. A feedback finite element method with a-posteriori error estimation: Part I. The finite element method and some basic properties of the a posteriori error estimator. Comput. Meth. Appl. Mech. Engrg. 61:1987;1-40.
18. Oden J.T., Demkowicz L., Rachowicz W., Westermann T.A. Toward a universal h-p adaptive finite element strategy: Part 2. A posteriori error estimation. Comput. Meth. Appl. Mech. Engrg. 77:1989;113-180.
19. B.A. Szabo, I. Babuška, Finite Element Analysis, Wiley, New York, 1991, pp.169-173.
20. Duff I.S., Reid J.K. The multifrontal solution of indefinite sparse symmetric linear systems. ACM Trans. Math. Softw. 9:1983;302-325.
21. I.S. Duff, J.K. Reid, MA47 - A Fortran code for direct solution of indefinite sparse symmetric linear systems, Report RAL-95-001, Rutherford Appleton Laboratory, Oxfordshire, 1995.
22. I.S. Duff, J.K. Reid, MA27 - A set of FORTRAN subroutines for solving sparse symmetric sets of linear equations, AERE R10533, HMSO, London, 1982.
23. J.N. Lyness, On handling singularities in finite elements, in: T.O. Espelid, A. Genz (Eds.), Numerical Integration, Recent Developments, Software and Applications, NATO ASI Series C. Math. Phys. Sci., vol. 357, Klewer Academic Publishers, The Netherlands, 1992.
24. Espelid T.O. On integrating vertex singularities using extrapolation. BIT. 34:1994;62-79.
25. Espelid T.O., Genz A. DECUHR: An algorithm for automatic integration of singular functions over a hyperrectangular region. Numer. Alg. 8:1994;201-220.
26. Berntson J., Espelid T.O., Genz A. An adaptive algorithm for the approximate calculation of multiple integrals. ACM Trans. Math. Softw. 17:1991;437-451.
27. G. Booch, Object Oriented Design with Applications, Benjamin/Cummings, New York, 1991, p. 100.