Meshless Galerkin method based on regions partitioned into subdomains

Applied Mathematics and Computation

Volumn 162, Issue 1, 2005, Pages 317-327

  Duan, Yong ^a   Tan, Yong Ji ^a  

^a FUDAN UNIVERSITY   (China)

Author keywords

Domain decomposition; Meshless; Parallel; RBF

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; ERROR ANALYSIS; FINITE ELEMENT METHOD; FUNCTION EVALUATION; INTERPOLATION; MATHEMATICAL OPERATORS; PARTIAL DIFFERENTIAL EQUATIONS; STIFFNESS MATRIX;

DOMAIN DECOMPOSITION METHOD (DDM); MESHLESS GALERKIN METHOD; MULTIVARIATE APPROXIMATION THEORY; RADIAL BASIS FUNCTIONS (RBF);

GALERKIN METHODS;

EID: 10444259743     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2003.12.138     Document Type: Article

References (13)

1. P.E. Bjørstad, O.B. widlund, Iterative methods for the solution of elliptic problems on regions partitioned into substructures, SIAM J. Numer. Anal. 23 (1986) 1097-1120.
2. J.H. Bramble, J.E. Pasciak, A.H. Schatz, An iterative method for elliptic problems on regions partitioned into substructures, Math. Comput. 46 (1986) 361-369.
3. C. Bernardi, Y. Maday, A.T. Petera, A new nonconforming approach to domain decomposition: the mortar element method, in: Nonlinear Partial Differential Equations and Their Applications, in: H. Brezis, J.-L. Lions (Eds.), Collège de France Seminar, vol. XI, Longman, Harlow, 1994, pp. 13-51.
4. T.F. Chan, T.P. Mathew, Domain decomposition algorithms, Acta. Numer. (1994) 143-161.
5. A. Quarteroni, A. Valli, Domain Decomposition Method for Partial Differential Equation, Oxford University Press, England, 1999.
6. T. Belytschko, Y. Krongauze, D. Organ, M. Fleming, P. Krysl, Meshless methods: an overview and recent developments, Comput. Methods Appl. Mech. Eng. 139 (1996) 3-47, special issue on Meshless Methods.
7. H. Wendland, Meshless Galerkin methods using radial basis functions, Math. Comput. 68 (1999) 1521-1531.
8. H. Wendland, Sobolev-type error estimates for interpolation by radial basis functions, in: A. LeMéhauté, C. Rabut, L.L. Schumaker (Eds.), Surface Fitting and Multiresolution Methods, Vanderbilt University Press, Nashville, 1997, pp. 337-344.
9. H. Wendland, Error estimates for interpolation by compactly supported radial basis functions of minimal degree, J. Approx. Theory 93 (1998) 258-272.
10. Z. Wu, R. Schaback, Local error estimates for radial basis function interpolation of scattered data, IMA J. Numer. Anal. (13) (1993) 13-27.
11. Z. Wu, Compactly supported positive definite radial functions, Adv. Comput. Math. 4 (1995) 283-292.
12. Zhi-jie Cai, Error estimate for elementfree Galerkin methods, preprint, 2003.
13. Ph.G. Ciarlet, J.L. Lions (Eds.), Basic Error Estimates for Elliptic Problems, Handbook of Numerical Analysis, vol. II. Finite Element Methods (part1), Elsevier, 1991.