Advances in Computational Mathematics

, Volume 9, Issue 3, pp 251–279

On the approximation power of bivariate splines

  • Ming-Jun Lai
  • Larry L. Schumaker

DOI: 10.1023/A:1018958011262

Cite this article as:
Lai, M. & Schumaker, L.L. Advances in Computational Mathematics (1998) 9: 251. doi:10.1023/A:1018958011262


We show how to construct stable quasi-interpolation schemes in the bivariate spline spaces Sdr(Δ) with d⩾ 3r + 2 which achieve optimal approximation order. In addition to treating the usual max norm, we also give results in the Lp norms, and show that the methods also approximate derivatives to optimal order. We pay special attention to the approximation constants, and show that they depend only on the smallest angle in the underlying triangulation and the nature of the boundary of the domain.

bivariate splinesapproximation order by splinesstable approximation schemessuper-splines41A1541A6341A2565D10

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Ming-Jun Lai
    • 1
  • Larry L. Schumaker
    • 2
  1. 1.Department of MathematicsThe University of GeorgiaAthensUSA
  2. 2.Department of MathematicsVanderbilt UniversityNashvilleUSA