We construct norming meshes with cardinality O(nˆs), s= 3, for polynomials of total degree at most n, on the closure of bounded planar Lipschitz domains. Such cardinality is intermediate between optimality (s= 2), recently obtained by Kroo on multidimensional Cˆ2 starlike domains, and that arising from a general construction on Markov compact sets due to Calvi and Levenberg (s= 4).
Suboptimal Polynomial Meshes on Planar Lipschitz Domains
PIAZZON, FEDERICO;VIANELLO, MARCO
2014
Abstract
We construct norming meshes with cardinality O(nˆs), s= 3, for polynomials of total degree at most n, on the closure of bounded planar Lipschitz domains. Such cardinality is intermediate between optimality (s= 2), recently obtained by Kroo on multidimensional Cˆ2 starlike domains, and that arising from a general construction on Markov compact sets due to Calvi and Levenberg (s= 4).
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