Corpus ID: 235457993

# On the stability of the L2 projection and the quasiinterpolant in the space of smooth periodic splines

@article{Dougalis2021OnTS,
title={On the stability of the L2 projection and the quasiinterpolant in the space of smooth periodic splines},
author={D. A. Dougalis},
journal={ArXiv},
year={2021},
volume={abs/2106.09060}
}
In this paper we derive stability estimates in Land L∞based Sobolev spaces for the L projection and a family of quasiinterolants in the space of smooth, 1-periodic, polynomial splines defined on a uniform mesh in [0, 1]. As a result of the assumed periodicity and the uniform mesh, cyclic matrix techniques and suitable decay estimates of the elements of the inverse of a Gram matrix associated with the standard basis of the space of splines, are used to establish the stability results.
1 Citations
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It is proved that the semidiscrete problem is well posed, locally in time, and satisfies a discrete positivity property for the water depth. Expand

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