Convergence of corrected derivative methods for second-order linear partial differential equations

International Journal for Numerical Methods in Engineering

Volumn 44, Issue 2, 1999, Pages 177-203

  Black, T ^a   Belytschko, T ^a,b  

^a NORTHWESTERN UNIVERSITY   (United States)

^b Northwestern University   (United States)

Author keywords

Completeness; Convergence; Meshfree

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; INTERPOLATION; NUMERICAL ANALYSIS;

COMPLETENESS;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0032761626     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19990120)44:2<177::AID-NME498>3.0.CO;2-1     Document Type: Article

References (12)

1. T. Belytschko, Y. Krongauz, D. Organ, M. Fleming and P. Krysl, 'Meshless methods: an overview and recent developments', Comput. Meth. Appl. Mech. Engng., 139, 3-47 (1996).
2. P. Krysl and T. Belytschko, 'Element-free Galerkin method: convergence of the continuous and discontinuous shape functions', Comput. Meth. Appl. Mech. Engng., 148, 257-277 (1997).
3. T. Belytschko, Y. Krongauz, J. Dolbow and C. Gerlach, 'On the completeness of particle and other meshfree methods', Int. J. Numer. Meth. Engng., in press.
4. G. R. Johnson and S. R. Beissel, 'Normalized smoothing functions for SPH impact calculations', Int. J. Numer. Meth. Engng., 1996.
5. P. Randles and L. Libersky, 'Smoothed Particle Hydrodynamics: Some recent improvements and applications', Comput. Meth. Appl. Mech. Engng., 139, 375-408 (1996).
6. T. Belytschko, Y. Y. Lu and L. Gu, 'Element-free Galerkin methods', Int. J. Numer. Meth. Engng., 37, 229-256 (1994).
7. Y. Krongauz and T. Belytschko, 'Consistent pseudo-derivatives in meshless methods', Comput. Meth. Appl. Mech. Engng., 146, 371-386 (1997).
8. J. M. Melenk and I. Babuška, 'The partition of unity finite element method: Basic theory and applications', Comput. Meth. Appl. Mech. Engng., 39, 289-314.
9. C. Duarte and J. Oden, 'hp clouds - a meshless method to solve boundary-value problems', Comput. Meth. Appl. Mech. Engng., 139, 237-262 (1996).
10. T. Belytschko, D. Organ and Y. Krongauz, 'A coupled finite element-element-free Galerkin method', Comput. Mech., 17, 186-195 (1995).
11. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, Springer, New York, 1991.
12. MATLAB User's Guide, The Math Works Inc., Natick, Massachusetts, A. Aziz and I. Babuška, Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, Academic Press, New York, 1972.