TY - JOUR

T1 - Optimal bounds for a Lagrange interpolation inequality for piecewise linear continuous finite elements in two space dimensions

AU - Muhamadiev, Èrgash

AU - Nazarov, Murtazo

N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: The second author is supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2015/3

Y1 - 2015/3

N2 - © 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.

AB - © 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.

UR - http://hdl.handle.net/10754/599087

UR - https://linkinghub.elsevier.com/retrieve/pii/S0022247X14009548

UR - http://www.scopus.com/inward/record.url?scp=84922511687&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2014.10.027

DO - 10.1016/j.jmaa.2014.10.027

M3 - Article

VL - 423

SP - 940

EP - 955

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -