A Petrov-Galerkin method with quadrature for elliptic boundary value problems

IMA Journal of Numerical Analysis

Volumn 24, Issue 1, 2004, Pages 157-177

  Bialecki, B ^a   Ganesh, M ^b   Mustapha, K ^b  

^a Department of Metallurgical and Materials Engineering   (United States)

^b UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Elliptic boundary value problems; Gauss quadrature; Petrov Galerkin method; Splines

Indexed keywords

ERROR ANALYSIS; GALERKIN METHODS; SPLINES;

APPROXIMATE SOLUTION; ELLIPTIC BOUNDARY VALUE PROBLEM; EXISTENCE AND UNIQUENESS; GAUSS QUADRATURES; OPTIMAL ORDERING; PETROV-GALERKIN METHODS; RECTANGULAR DOMAIN; VARIABLE COEFFICIENTS;

BOUNDARY VALUE PROBLEMS;

EID: 1642458377     PISSN: 02724979     EISSN: None     Source Type: Journal    
DOI: 10.1093/imanum/24.1.157     Document Type: Article

References (18)

1. BIALECKI, B. (1998) Convergence analysis of orthogonal spline collocation for elliptic boundary value problems. SIAM J. Numer. Anal., 35, 617-631.
2. BIALECKI, B. & FAIRWEATHER, G. (2001) Orthogonal spline collocation methods for partial differential equations. J. Comput. Appl. Math., 128, 55-85.
3. BOTTCHER, C. & STRAYER, M. R. (1990) The basis spline method and associated techniques. Computational Atomic and Nuclear Physics. (C. Bottcher, M. R. Strayer & J. B. McGrory, eds). Singapore: World Scientific, pp. 217-240.
4. BOTTCHER, C. & STRAYER, M. R. (1993) Spline methods for conservation equations. Computational Acoustics - Volume 2. (D. Lee, A. R. Robinson & R. Vichnevetsky, eds). Amsterdam: Elsevier, pp. 317-338.
5. BRAMBLE, J. H. & HILBERT, S. R. (1971) Bounds for a class of linear functional with applications to Hermite interpolation. Numer. Math., 16, 362-369.
6. BRAMBLE, J. H., EWING, R. E. & LI, G. (1989) Alternating direction multistep methods for parabolic problems-iterative stabilization. SIAM J. Numer. Anal., 26, 904-919.
7. DE BOOR, C. (1966) The method of projections as applied to the numerical solution of the two point boundary value problems using cubic splines. Ph.D. Thesis, University of Michigan.
8. DOUGLAS, J. & DUPONT, T. (1974) Collocation Method for Parabolic Equations in a Single Space Variable. Lecture Notes in Mathematics 385. New York: Springer.
9. -1 Galerkin procedures for elliptic equations. RAIRO Anal. Numér., 11, 3-12.
10. GRIGORIEFF, R. D. & SLOAN, I. H. (1996) Spline Petrov-Galerkin methods with quadrature. Numer. Funct. Anal. Optimiz., 17, 755-784.
11. HADJIDIMOS, A., HOUSTIS, E. N., RICE, J. R. & VAVALIS, E. (1999) Analysis of iterative line cubic spline collocation methods for elliptic partial differential equations. SIAM J. Matrix Anal. Appl., 21, 508-521.
12. 4) cubic spline collocation methods for elliptic partial differential equations. SIAM J. Numer. Anal., 25, 54-74.
13. KEGLEY, JR, D. R., OBERACKER, V. E., STRAYER, M. R., UMAR, A. S. & WELLS, J. C. (1996) Basis spline collocation method for solving the Schrödinger equation in axillary symmetric systems. J. Comput. Phys., 128, 197-208.
14. FAIRWEATHER, G. (1978) Finite Element Galerkin Methods for Differential Equations, Lecture Notes in Pure and Applied Mathematics 34. New York: Dekker.
15. SLOAN, I. H., TRAN, D. & FAIRWEATHER, G. (1993) A fourth-order cubic spline method for linear second-order two-point boundary value problems. IMA J. Numer. Anal., 13, 591-607.
16. TSOMPANOPOULOU, P. & VAVALIS, E. (1998) ADI methods for cubic spline collocation discretizations of elliptic PDEs. SIAM J. Sci. Comput., 19, 341-363.
17. UMAR, A. S. (1990) Three-dimensional HF and TDHF calculations with the basis-spline collocation technique. Computational Atomic and Nuclear Physics. (C. Bottcher, M. R. Strayer & J. B. McGrory, eds). Singapore: World Scientific, pp. 377-390.
18. UMAR, A. S., WU, J., STRAYER, M. R. & BOTTCHER, C. (1991) Basis-spline collocation method for the lattice solution of boundary value problems. J. Comput. Phys., 93, 426-448.