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

Handle URI:
http://hdl.handle.net/10754/599087
Title:
Optimal bounds for a Lagrange interpolation inequality for piecewise linear continuous finite elements in two space dimensions
Authors:
Muhamadiev, Èrgash; Nazarov, Murtazo
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<sup>-2</sup>, where p is a polynomial degree, that goes fast to zero as p increases. We prove that the lower bound is proportional to ln<sup>2</sup> p which is an increasing function. Moreover, we prove that this estimate is sharp.
Citation:
Muhamadiev È, Nazarov M (2015) Optimal bounds for a Lagrange interpolation inequality for piecewise linear continuous finite elements in two space dimensions. Journal of Mathematical Analysis and Applications 423: 940–955. Available: http://dx.doi.org/10.1016/j.jmaa.2014.10.027.
Publisher:
Elsevier BV
Journal:
Journal of Mathematical Analysis and Applications
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
Mar-2015
DOI:
10.1016/j.jmaa.2014.10.027
Type:
Article
ISSN:
0022-247X
Sponsors:
The second author is supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorMuhamadiev, Èrgashen
dc.contributor.authorNazarov, Murtazoen
dc.date.accessioned2016-02-25T13:52:37Zen
dc.date.available2016-02-25T13:52:37Zen
dc.date.issued2015-03en
dc.identifier.citationMuhamadiev È, Nazarov M (2015) Optimal bounds for a Lagrange interpolation inequality for piecewise linear continuous finite elements in two space dimensions. Journal of Mathematical Analysis and Applications 423: 940–955. Available: http://dx.doi.org/10.1016/j.jmaa.2014.10.027.en
dc.identifier.issn0022-247Xen
dc.identifier.doi10.1016/j.jmaa.2014.10.027en
dc.identifier.urihttp://hdl.handle.net/10754/599087en
dc.description.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<sup>-2</sup>, where p is a polynomial degree, that goes fast to zero as p increases. We prove that the lower bound is proportional to ln<sup>2</sup> p which is an increasing function. Moreover, we prove that this estimate is sharp.en
dc.description.sponsorshipThe second author is supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherElsevier BVen
dc.subjectConvergenceen
dc.subjectFinite elementsen
dc.subjectInequalityen
dc.subjectLagrange interpolation estimatesen
dc.subjectScalar conservation lawsen
dc.titleOptimal bounds for a Lagrange interpolation inequality for piecewise linear continuous finite elements in two space dimensionsen
dc.typeArticleen
dc.identifier.journalJournal of Mathematical Analysis and Applicationsen
dc.contributor.institutionVologda State University, Vologda, Russian Federationen
dc.contributor.institutionUppsala Universitet, Uppsala, Swedenen
kaust.grant.numberKUS-C1-016-04en
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