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
SN - 0022-247X
VL - 423
SP - 940
EP - 955
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -