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Register a new userOn the stability of the $L^{2}$ projection and the quasiinterpolant in the space of smooth periodic splines
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Added by
Dimitrios Antonopoulos
Publication date
2021
fields
Informatics Engineering
and research's language is
English
Authors
D.C. Antonopoulos V.A. Dougalis
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In this paper we derive stability estimates in $L^{2}$- and $L^{infty}$- based Sobolev spaces for the $L^{2}$ 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.
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