Optimal bounds for a Lagrange interpolation inequality for piecewise linear continuous finite elements in two space dimensions

Èrgash Muhamadiev, Murtazo Nazarov

Research output: Contribution to journalArticlepeer-review

Abstract

© 2014 Elsevier Inc. In this paper the interpolation inequality of Szepessy [12, Lemma 4.2] is revisited. The lower bound in the above reference is proven to be proportional to p$^{-2}$, where p is a polynomial degree, that goes fast to zero as p increases. We prove that the lower bound is proportional to ln$^{2}$ p which is an increasing function. Moreover, we prove that this estimate is sharp.
Original languageEnglish (US)
Pages (from-to)940-955
Number of pages16
JournalJournal of Mathematical Analysis and Applications
Volume423
Issue number2
DOIs
StatePublished - Mar 2015
Externally publishedYes

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