A posteriori error approximation in EFG method

International Journal for Numerical Methods in Engineering

Volumn 58, Issue 15, 2003, Pages 2239-2263

  Gavete, L ^a   Gavete, M L ^b   Alonso, B ^a   Martin A J ^a  

^a Dpto de Automatic Ingenieria Electronica e Informatics Industrial DISAM   (Spain)

^b UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

Element free Galerkin method; Error approximation; Meshless; Moving least squares

Indexed keywords

ELASTICITY; ERROR ANALYSIS; FINITE ELEMENT METHOD; GALERKIN METHODS; LEAST SQUARES APPROXIMATIONS; PARAMETER ESTIMATION;

ELEMENT FREE GALERKIN (EFG) METHOD; MESHLESS METHODS;

COMPUTATIONAL METHODS;

MATHEMATICAL METHOD;

EID: 0346304802     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.850     Document Type: Article

References (24)

1. Monaghan JJ. Why particle methods work. SIAM Journal on Scientific and Statistical Computing 1982; 3:422-433.
2. Monaghan JJ. An introduction to SPH. Computer Physics Communications 1988; 48:89-96.
3. Perrone N, Kao R. A general finite difference method for arbitrary meshes. Computers and Structures 1975; 5:45-58.
4. Liszka T, Orkisz J. The finite difference method at arbitrary irregular grids and its application in applied mechanics. Computers and Structures 1980; 11:83-95.
5. Orkisz J. Meshless finite difference method II. Adaptative approach. In Computational Mechanics, Idelsohn S, Onate E, Dvorkin (eds). CIMNE: Buenos Aires, Argentina, 1998.
6. Lancaster P, Salkauskas K. Surfaces generated by moving least squares methods. Mathematics of Computation 1981; 37:141-158.
7. Nayroles B, Touzot G, Villon P. Generalizing the finite element method: diffuse approximation and diffuse elements. Computational Mechanics 1992; 10:307-318.
8. Belytschko T, Lu YY, Gu L. Element-free Galerkin methods. International Journal for Numerical Methods in Engineering 1994; 37:229-256.
9. Lu YY, Belytschko T, Gu L. A new implementation of the element-free Galerkin method. Computer Methods in Applied Mechanics and Engineering 1994; 113:397-414.
10. Liu WK, Jun S, Li S, Adee J, Belytschko T. Reproducing kernel particle methods for structural dynamics. International Journal for Numerical Methods in Engineering 1995; 38:1655-1679.
11. Duarte A, Oden JT. H-P Cloud-An h-p meshless method. Numerical Methods for Partial Differential Equations 1996; 12:673-705.
12. Babuska I, Melenk JM. The partition of unity method. International Journal for Numerical Methods in Engineering 1997; 40:727-758.
13. Onate E, Idelsohn S, Zienkiewicz OC, Taylor RL. A finite point method in computational mechanics. Applications to convective transport and fluid flow. International Journal for Numerical Methods in Engineering 1996; 39:3839-3866.
14. Gavete L, Benito JJ, Falcon S, Ruiz A. Implementation of essential boundary conditions in a meshless method. Communications in Numerical Methods in Engineering 2000; 16:409-421.
15. Krongauz Y, Belytschko T. A Petrov-Galerkin diffuse element method (PG DEM) and its comparison to EFG. Computational Mechanics 1997; 19:327-333.
16. Mukherjee YX, Mukherjee S. On boundary conditions in the element-free Galerkin method. Computational Mechanics 1997; 19:264-270.
17. Duarte A, Oden JT. An h-p adaptive method using clouds. TICAM Report 96-07. University of Texas: Austin, 1996.
18. Laouar T, Villon P. Adaptative analysis for the diffuse element method. In Computational Mechanics, Idelhson S, Onate E, Dvorkin (eds). CIMNE: Buenos Aires, Argentina, 1998.
19. Gavete L, Falcón S, Ruiz A. Some results on the diffuse approximation using Galerkin method. In II ECCOMAS Conference on Numerical Methods in Engineering, ECCOMAS96. Wiley: Paris, 1996; 499-505.
20. Gavete L, Falcón S, Ruiz A. An error indicator for the element free Galerkin method. European Journal of Mechanics - A/Solids 2001; 20:327-341.
21. Gavete L, Cuesta JL, Ruiz A. A procedure for approximation of the error in EFG method. International Journal for Numerical Methods in Engineering 2002; 53:677-690.
22. Chung H-J, Belytschko T. An error estimate in the EFG method. Computational Mechanics 1998; 21:91-100.
23. Liu WK, Li S, Belytschko T. Reproducing least square kernel Galerkin method. (i) Methodology and convergence. Computer Methods in Applied Mechanics and Engineering 1997; 143:422-433.
24. Timoshenko S, Goodier JN. Theory of Elasticity. McGraw-Hill: New York, 1987.