Higher Order B-Spline Collocation at the Greville Abscissae

Journal Article · Sat Jan 01 04:00:00 EST 2005 · Applied Numerical Mathematics

DOI:https://doi.org/10.1016/j.apnum.2004.04.002· OSTI ID:912034

Johnson, Richard Wayne

Collocation methods are investigated because of their simplicity and inherent efficiency for application to a model problem with similarities to the equations of fluid dynamics. The model problem is a steady, one-dimensional convection-diffusion equation with constant coefficients. The objective of the present research is to compare the efficiency and accuracy of several collocation schemes as applied to the model problem for values of 15 and 50 for the associated Peclet number. The application of standard nodal and orthogonal collocation is compared to the use of the Greville abscissae for the collocation points, in conjunction with cubic and quartic B-splines. The continuity of the B-spline curve solution is varied from C1 continuity for traditional orthogonal collocation of cubic and quartic splines to C2-C3 continuity for cubic and quartic splines employing nodal, orthogonal and Greville point collocation. The application of nodal, one-point orthogonal, and Greville collocation for smoothest quartic B-splines is found to be as accurate as for traditional two-point orthogonal collocation using cubics, while having comparable or better efficiency based on operation count. Greville collocation is more convenient than nodal or 1-point orthogonal collocation because exactly the correct number of collocation points is available.

• Research Organization: Idaho National Laboratory (INL)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC07-99ID13727
• OSTI ID: 912034
• Report Number(s): INEEL/JOU-02-00165
• Journal Information: Applied Numerical Mathematics, Journal Name: Applied Numerical Mathematics Journal Issue: 1 Vol. 52
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
B-Spline
CALCULATION METHODS
COMPARATIVE EVALUATIONS
CONVECTION
DIFFUSION
Greville abscissae
ONE-DIMENSIONAL CALCULATIONS
collocation
fluid dynamics