Ritz-type projectors with boundary interpolation properties and explicit spline error estimates

TL;DR

This paper develops Ritz-type projectors with boundary interpolation in Sobolev spaces, providing explicit error estimates for spline spaces, advancing the understanding of approximation properties in numerical analysis.

Contribution

It introduces Ritz-type projectors with boundary interpolation properties and derives explicit a priori error estimates for spline spaces, extending previous work on classical Ritz projectors.

Findings

Explicit error constants for spline approximation

Boundary interpolation properties improve approximation accuracy

Extension of previous Ritz projector error estimates

Abstract

In this paper we construct Ritz-type projectors with boundary interpolation properties in finite dimensional subspaces of the usual Sobolev space and we provide a priori error estimates for them. The abstract analysis is exemplified by considering spline spaces and we equip the corresponding error estimates with explicit constants. This complements our results recently obtained for explicit spline error estimates based on the classical Ritz projectors in [Numer. Math. 144(4):889--929, 2020].