Moving least-square reproducing kernel methods (I) methodology and convergence

Computer Methods in Applied Mechanics and Engineering

Volumn 143, Issue 1-2, 1997, Pages 113-154

  Liu, Wing Kam ^a   Li, Shaofan ^a   Belytschko, Ted ^a  

^a Northwestern University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY VALUE PROBLEMS; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; ERROR ANALYSIS; FINITE ELEMENT METHOD; FUNCTIONS; INTERPOLATION; MATHEMATICAL OPERATORS; POLYNOMIALS;

GALERKIN METHOD; LEAST SQUARE INTERPOLATION; MOVING LEAST SQUARE REPRODUCING KERNEL (MLSRK) METHOD;

LEAST SQUARES APPROXIMATIONS;

EID: 0031119696     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(96)01132-2     Document Type: Article

References (27)

1. R.A. Gingold and J.J. Monaghan, Kernel estimates as a basis for general particle methods in hydrodynamics, J. Comput. Phys. 46 (1982) 429-453.
2. J.J. Monaghan, Why particle methods work, SIAM J. Scient. Stat. Comput. 3 (1982) 422-433.
3. B. Nayroles, G. Touzot and P. Villon, Generalizing the finite element method: Diffuse approximation and diffuse elements, Comput. Mech. 10 (1992) 307-318.
4. T. Belytschko, Y.Y. Lu and L. Gu, Element free Galerkin methods, Int. J. Numer. Methods Engrg. 37 (1994) 229-256.
5. T. Belytschko, L. Gu and Y.Y. Lu, Fracture and crack growth by element free Galerkin methods. Modelling Simul. Mater. Sci. Engrg. 2 (1994b) 519-534.
6. W.K. Liu, S. Jun and Y. Zhang, Reproducing kernel particle methods, Int. J. Numer. Methods Fluids 20 (1995) 1081-1106.
7. W.K. Liu and Y. Chen, Wavelet and multiple scale reproducing kernel methods, Int. J. Numer. Methods Fluids 21 (1995) 901-933.
8. W.K. Liu, S. Jun, S. Li, J. Adee and T. Belytschko, Reproducing kernel particle methods for structural dynamics, Int. J. Numer. Methods Engrg. 38 (1995) 1655-1679.
9. W.K. Liu, An introduction to wavelet reproducing kernel particle methods, USACM Bulletin 8(1) (1995) 3-16.
10. P. Lancaster and K. Salkauskas, Surfaces generated by moving least square methods, Math. Comput. 37(155) (1980) 141-158.
11. S. Li and W.K. Liu, Moving least square reproducing kernel method. Part II: Fourier analysis, Comput. Methods Appl. Mech. Engrg. 139 (1996) 159-194.
12. R.O. Wells Jr. and X. Zhou, Wavelet interpolation and approximate solutions of elliptic partial differential equations, (1993) preprint.
13. C.A. Duarte and J.T. Oden, Hp Clouds - a meshless method to solve boundary-value problems, (1995) preprint.
14. W. Rudin, Principles of Mathematical Analysis, 3rd edition (McGraw-Hill, Inc., 1976).
15. D.S. Mitrinovic, Analytic Inequalities (Springer-Verlag, Berlin, Heidelberg, New York, 1970).
16. P.J. Davis, Interpolation and Approximation (Dover Publications, Inc., New York, 1975).
17. C.K. Chui, An Introduction to Wavelet (Academic Press, New York, 1992).
18. I. Babuška and J.M. Melenk, The partition of unity finite element method, Technical Note BN-1185, Institute for Physical Science and Technology, University of Maryland, 1995.
19. C. de Boor and G.J. Fix, Spline approximation by quasi-interpolants, J. Approx. Theory 8 (1975) 19-45.
20. R.A. Horn and C.R. Johnson, Matrix Analysis (Cambridge University Press, 1985).
21. G.H. Golub and C.F. Van Loan, Matrix Computations, 2nd edition (The Johns Hopkins University Press, Baltimore, MD, 1989).
22. P.G. Ciarlet, The Finite Element Method For Elliptic Problems (North-Holland Publishing Company, Amsterdam, New York, 1978).
23. I. Babuška, The finite element method with Lagrangian multipliers, Numer. Math. (20)(1973) 179-192.
24. T.J.R. Hughes, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis (Prentice Hall, Englewood Cliffs, NJ, 1987).
25. -1-Galerkin procedure for the two-point boundary value, in: C. de Boor, ed., Mathematical Aspects of Finite Elements in Partial Differential Equations (Academic Press, New York, 1974).
26. I. Babuška, J.T. Oden and J.K. Lee, Mixed-hybrid finite element approximations of second-order elliptic boundary-value problems, Comput. Methods Appl. Mech. Engrg. 11 (1977) 175-206.
27. I. Daubechies, Wavelets, CBMS-NSF Series in Applied Mathematics (SIAM Publication, Philadelphia, 1992).