A posteriori error estimation and adaptive node refinement for fast moving least square reproducing kernel (FMLSRK) method

CMES - Computer Modeling in Engineering and Sciences

Volumn 20, Issue 1, 2007, Pages 35-41

  Lee, Chany ^a   Im, Chang Hwan ^b   Jung, Hyun Kyo ^a   Kim, Hong Kyu ^c   Kim, Do Wan ^d  

^a Seoul National University   (South Korea)

^b Yonsei University Wonju   (South Korea)

^c Korea Electrotechnology Research Institute (KERI)   (South Korea)

^d Hanyang University   (South Korea)

Author keywords

Adaptive node refinement; Electrostatics; Error estimation; Fast moving least square reproducing kernel (FMLSRK) method; Meshless methods

Indexed keywords

ADAPTIVE SYSTEMS; ELECTROSTATICS; ERROR ANALYSIS; LEAST SQUARES APPROXIMATIONS; PARAMETER ESTIMATION;

ADAPTIVE NODE REFINEMENT; FAST MOVING LEAST SQUARE REPRODUCING KERNEL (FMLSRK) METHODS; MESHLESS METHODS;

ELECTROMAGNETIC FIELD THEORY;

EID: 34547812048     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (19)

1. Atluri S.N., Kim H.G., Cho J.Y. (1999): A critical assessment of the truly meshless local Petrov-Galerkin(MLPG) and local boundary integral equation(LBIE) methods. Comput Mech, vol. 24, pp. 348-372.
2. Atluri S.N., Shen S. (2002): The meshless local Petrov-Galerkin(MLPG) method: A simple & Less-costly alternative to the finite element and boundary element methods. CMES: Computer Modeling in Engineering & Science, vol. 3(1): pp. 11-51.
3. Boroomand, B.; Zienkiewicz, O. C. (1997): Recovery by equilibrium in patches (REP) Int J Numer Meth Engng, vol. 40, pp. 137-164.
4. Bugeda, G. (2002): A comparison between new adaptive remeshing strategies based on point wise stress error estimation and energy norm error estimation. Commun Numer Meth Engng, vol. 18, pp. 469-482.
5. Duarte, C. A.; Oden, J. T. (1996): An h-p adaptive method using clouds. Comput Meth Appl Mech Eng, vol. 139, pp. 237-262.
6. Gingold, R. A.; Monaghan, J. J. (1997): Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon Not R astr Soc, vol. 181, pp. 375-389.
7. Gavete, L.; Cuesta, J. L.; Ruiz, A. (2002): A procedure for approximation of the error in the EFG method. Int J Numer Meth Engng, Vol. 53, pp. 677-690.
8. Janicke, L.; Kost A. (1996): Error estimation and adaptive mesh generation in the 2D and 3D finite element method. IEEE Trans Magn, vol. 32, No. 3, pp. 1334-1337.
9. Kim, D. W.; Kim, Y. (2003): Point collocation methods using the fast moving least-square reproducing kernel approximation. Int J Numer Meth Engng, vol. 56, pp.1445-1464.
10. Kim, D. W.; Kim, H. K. (2004): Point collocation method based on the FMLSRK approximation for electromagnetic field analysis. IEEE Trans Magn, vol. 40, no. 2, pp. 1029-1032.
11. Kvamsdal T.; Okstad, K. M. (1998): Error estimation based on superconvergent patch recovery using statically admissible stress fields. Int J Numer Meth Engng, vol. 42, pp. 443-472.
12. Lu, Y. Y.; Belytschko, T.: Gu, L. (1994): A new implementation of the element free Galerkin method. Comput Meth Appl Mech Eng, vol. 113, pp. 397-414.
13. Liu, W. K.; Jun, S.; Zhang, Y. F. (1995): Reproducing kernel particle methods. Int J Numer Meth Fl, vol. 20. pp. 1081-1106.
14. Liu, W. K.; Li, S; Belytschko, T. (1996): Moving least square reproducing kernel methods (I) methodology and convergence. Comput Meth Appl Mech Eng, vol. 143. pp. 422-433.
15. Lin H., Atluri S.N. (2000): Meshless local Petrov-Galerkin(MLPG) method for convection-diffusion problems. CMES: Computer Modeling in Engineering & Science, vol. 1(2): pp. 45-60.
16. Lin H., Atluri S.N. (2001): The meshless local Petrov-Galerkin(MLPG) method for solving incompressible Navier-Stokes equations. CMES: Computer Modeling in Engineering & Science, vol. 2(2): pp. 117-142.
17. Melenk, J. M.; Babuška, I. (1996): The partition of unity finite element method: basic theory and applications. Int J Numer Meth Engng, vol. 139. pp. 289-314.
18. Shu C., Ding H., Yeo K.S. (2005): Computation of incompressible Navier-Stokes equations by local RBF-based differential quadrature method. CMES: Computer Modeling in Engineering & Science, vol. 7(2): pp. 195-205.
19. Ubertini, F. (2004): Patch recovery based on complementary energy. Int J Numer Meth Engng, vol. 59, pp. 1501-1538.