On the L_p-error of adaptive approximation of bivariate functions by harmonic splines

Abstract

Interpolation by various types of splines is the standard procedure in many applications. In this paper we discuss harmonic spline “interpolation” (on the lines of a grid) as an alternative to polynomial spline interpolation (at vertices of a grid). We will discuss some advantages and drawbacks of this approach and present the asymptotics of the -error for adaptive approximation by harmonic splines.

Keywords:

• interpolation
• adaptive
• harmonic spline
• optimal error
• asymptotics

AMS Subject Classifications:

• 41A15
• 41A60
• 68W25
• 97N50

Acknowledgments

Authors would like to thank Professor V. Babenko for his advice and guidance during work on this project.