A Galerkin boundary node method and its convergence analysis

Journal of Computational and Applied Mathematics

Volumn 230, Issue 1, 2009, Pages 314-328

  Li, Xiaolin ^a   Zhu, Jialin ^a  

^a CHONGQING UNIVERSITY   (China)

Author keywords

Galerkin boundary node method; Galerkin's method; Meshless; Moving least squares; Pseudo differential operator

Indexed keywords

GALERKIN BOUNDARY NODE METHOD; GALERKIN'S METHOD; MESHLESS; MOVING LEAST-SQUARES; PSEUDO-DIFFERENTIAL OPERATOR;

AIRCRAFT LANDING SYSTEMS; BOUNDARY CONDITIONS; BOUNDARY INTEGRAL EQUATIONS; COMPUTATIONAL FLUID DYNAMICS; ERROR ANALYSIS; FUNCTION EVALUATION; LAPLACE EQUATION; MATHEMATICAL OPERATORS;

GALERKIN METHODS;

EID: 67349131583     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2008.12.003     Document Type: Article

References (28)

1. Belytschko T., Krongauz Y., Organ D., Fleming M., and Krysl P. Meshless methods: An overview and recent developments. Comput. Methods Appl. Mech. Eng. 139 (1996) 3-47
2. Liu G.R. Meshfree Methods-Moving Beyond the Finite Element Method (2002), CRC Press, Boca Raton
3. Krysl P., and Belytschko T. Element-free Galerkin method: Convergence of the continuous and discontinuous shape functions. Comput. Methods Appl. Mech. Eng. 148 (1997) 257-277
4. Han W., and Meng X. Error analysis of the reproducing kernel particle method. Comput. Methods Appl. Mech. Eng. 190 (2001) 6157-6181
5. Li S., and Liu W.K. Moving least-square reproducing kernel methods Part II: Fourier analysis. Comput. Methods Appl. Mech. Eng. 139 (1996) 159-193
6. Liu W.K., Li S., and Belytschko T. Moving least-square reproducing kernel methods (I) Methodology and convergence. Comput. Methods Appl. Mech. Eng. 143 (1997) 113-154
7. Cheng R., and Cheng Y. Error estimates for the finite point method. Appl. Numer. Math. 58 (2008) 884-898
8. Duarte C.A., and Oden J.T. H-p clouds-An h-p meshless method. Numer. Methods Partial Differential Equations 12 (1996) 675-705
9. Lancaster P., and Salkauskas K. Surface generated by moving least squares methods. Math. Comp. 37 (1981) 141-158
10. Shepard D. A two-dimensional interpolation function for irregularly spaced points. Proc. 23rd Nat. Conf. ACM (1968), ACM Press, New York 517-524
11. Mukherjee Y.X., and Mukherjee S. The boundary node method for potential problems. Internat. J. Numer. Methods Eng. 40 (1997) 797-815
12. Xie H., Nogami T., and Wang J. A radial boundary node method for two-dimensional elastic analysis. Eng. Anal. Bound. Elem. 27 (2003) 853-863
13. Golberg M.A., Chen C.S., and Bowman H. Some recent results and proposals for the use of radial basis functions in the BEM. Eng. Anal. Bound. Elem. 23 (1999) 285-296
14. Brenner S.C., and Scott L.R. The Mathematical Theory of Finite Element Methods (1994), Springer-Verlag, New York
15. Lious J.L., and Magenes E. Non-Homogeneous Boundary Value Problems and Applications (1972), Springer-Verlag, Berlin
16. Kufner A. Weighted Sobolev Spaces (1985), Wiley, New York
17. Zuppa C. Good quality point sets and error estimates for moving least square approximations. Appl. Numer. Math. 47 (2003) 575-585
18. Armentano M.G., and Duran R.G. Error estimates for moving least-square approximations. Appl. Numer. Math. 37 (2001) 397-416
19. Zuppa C. Error estimates for moving least-square approximations. Bull Braz. Math. Soc. (N.S.) 34 (2003) 231-249
20. Zuppa C. Jackson-type inequalities for h-p clouds and error estimates. Comput. Methods Appl. Mech. Eng. 194 (2005) 1875-1887
21. Hsiao G.C. Boundary element methods-An overview. Appl. Numer. Math. 56 (2006) 1356-1369
22. Wendland W.L. Boundary element methods for elliptic problems. In: Schatz A.H., Thomée V., and Wendland W.L. (Eds). Mathematical Theory of Finite and Boundary Element Methods (1990), Birkhäuser Verlag, Boston 223-269
23. Zhu J. Boundary Element Analysis for Elliptic Boundary Value Problems (1991), Science Press, Beijing
24. Kane J.H. Boundary Element Analysis in Engineering Continuum Mechanics (1994), Prentice Hall, New Jersey
25. Nicolazzi L.C., Barcellos C.S., Fancello E.A., and Duarte C.A.M. Generalized boundary element method for galerkin boundary integrals. Eng. Anal. Bound. Elem. 29 (2005) 494-510
26. Zhu J., and Zhang S. Galerkin boundary element method for solving the boundary integral equation with hypersingularity. J. Univ. Sci. Technol. China 37 (2007) 1357-1362
27. 3. Comput. Methods Appl. Mech. Eng. 8 (1976) 61-86
28. Nedelec J.C., Artola M., and Cessenat M. Integral equations and numerical methods. In: Dautray R., and Lious J.L. (Eds). Mathematical Analysis and Numerical Methods for Science and Technology vol. 4 (2000), Springer, Berlin 33-152