Bounds on projections onto bivariate polynomial spline spaces with stable local bases

Constructive Approximation

Volumn 18, Issue 2, 2002, Pages 241-254

  Von Golitschek, Manfred ^a   Schumaker, Larry L ^b  

^a UNIVERSITY OF WÜRZBURG   (Germany)

^b VANDERBILT UNIVERSITY   (United States)

Author keywords

Bivariate splines; Norms of projections; Spline approximation

Indexed keywords

EID: 0036011648     PISSN: 01764276     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00365-001-0018-4     Document Type: Article

References (19)

1. P. ALFELD, M. NEAMTU, L. L. SCHUMAKER (1996): Fitting scattered data on sphere-like surfaces using spherical splines. J. Comput. Appl. Math., 73:5-43.
2. P. ALFELD, L. L. SCHUMAKER (to appear): Smooth macro elements based on Clough-Tocher triangle splits. Numer. Math.
3. P. ALFELD, L. L. SCHUMAKER (to appear): Smooth macro elements based on Powell-Sabin triangle splits. Adv. in Comput. Math.
4. 2-approximation by splines in terms of a global mesh ratio. Math. Comp., 30(136):765-771.
5. C. DE BOOR (1981): On a max-norm bound for the least-squares spline approximant. In: Approximation and Function Spaces (C. Ciesielski, ed.). Amsterdam: North-Holland, pp. 163-175.
6. C. K. CHUI, DONG HONG, RONG-QING JIA (1995): Stability of optimal order approximation by bivariate splines over arbitrary triangulations. Trans. Amer. Math. Soc., 347:3301-3318.
7. S. DEMKO (1977): Inverses of band matrices and local convergence of spline projections. SIAM J. Numer. Anal., 14:616-619.
8. J. DESCLOUX (1972): On finite element matrices. SIAM J. Numer. Anal., 9:260-265.
9. O. DAVYDOV, L. L. SCHUMAKER (2002): On stable local bases for bivariate polynomial spline spaces. Constr. Approx., 18:87-116.
10. O. DAVYDOV, L. L. SCHUMAKER (2000): Locally linearly independent bases for bivariate polynomial splines. Adv. in Comput. Math., 13:355-373.
11. J. DOUGLAS JR., T. DUPONT, L. WAHLBIN (1975): Optimal L∞ error estimates for Galerkin approximations to solutions of two-point boundary value problems. Math. Comp., 29:475-483.
12. 2 projection into finite element function spaces. Numer. Math., 23:193-197.
13. M. VON GOLITSCHEK (2000): Norms of projectors onto spaces with Riesz bases. J. Comput. Appl. Math., 119:209-221.
14. M. VON GOLITSCHEK, M.-J. LAI, L. L. SCHUMAKER (to appear): Error bounds for minimal energy bivariate polynomial splines. Numer. Math.
15. M. J. LAI, L. L. SCHUMAKER (1993): On the approximation power of splines on triangulated quadrangulations. SIAM J. Numer. Anal., 36:143-159.
16. M. J. LAI, L. L. SCHUMAKER (1998): On the approximation power of bivariate splines. Adv. in Comput. Math., 9:251-279.
17. M. J. LAI, L. L. SCHUMAKER (to appear): Macro-elements and stable local bases for splines on Powell-Sabin triangulations. Math. Comp.
18. M. J. LAI, L. L. SCHUMAKER (to appear): Macro-elements and stable local bases for splines on Clough-Tocher triangulations. Numer. Math.
19. M. NEAMTU, L. L. SCHUMAKERJ (to appear): On the approximation power of spherical splines.