### Espen Sande, Roma Tor Vergata

Sala conferenze IMATI-CNR, Pavia – Martedì 19 Novembre 2019 h.15:00

Abstract. In this talk we provide a priori error estimates with explicit constants for both the $L^2$-projection and the Ritz projection onto spline spaces of arbitrary smoothness defined on arbitrary grids. This extends and completess the results recently obtained for spline spaces of maximal smoothness.

The presented error estimates indicate that smoother spline spaces exhibit a better approximation behavior per degree of freedom, even for low smoothness of the functions to be approximated. This is in complete
agreement with the numerical evidence found in the literature.

We begin with presenting results for univariate spline spaces, and then we address multivariate tensor-product spline spaces and isogeometric spline spaces generated by means of a mapped geometry, both in the single-patch and in the multi-patch case.