This paper introduces a quasi-interpolation operator for scalar- and vector-valued finite element spaces constructed on affine, shape-regular meshes with some continuity across mesh interfaces. This operator gives optimal estimates of the best approximation error in any -norm assuming regularity in the fractional Sobolev spaces , where and the smoothness index can be arbitrarily close to zero. The operator is stable in , leaves the corresponding finite element space point-wise invariant, and can be modified to handle homogeneous boundary conditions. The theory is illustrated on -, - and -conforming spaces.
Accepté le :
DOI : 10.1051/m2an/2016066
Mots clés : Quasi-interpolation, finite elements, best approximation
@article{M2AN_2017__51_4_1367_0,
author = {Ern, Alexandre and Guermond, Jean-Luc},
title = {Finite element quasi-interpolation and best approximation},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1367--1385},
publisher = {EDP-Sciences},
volume = {51},
number = {4},
year = {2017},
doi = {10.1051/m2an/2016066},
mrnumber = {3702417},
zbl = {1378.65041},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2016066/}
}
TY - JOUR AU - Ern, Alexandre AU - Guermond, Jean-Luc TI - Finite element quasi-interpolation and best approximation JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 1367 EP - 1385 VL - 51 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2016066/ DO - 10.1051/m2an/2016066 LA - en ID - M2AN_2017__51_4_1367_0 ER -
%0 Journal Article %A Ern, Alexandre %A Guermond, Jean-Luc %T Finite element quasi-interpolation and best approximation %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 1367-1385 %V 51 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2016066/ %R 10.1051/m2an/2016066 %G en %F M2AN_2017__51_4_1367_0
Ern, Alexandre; Guermond, Jean-Luc. Finite element quasi-interpolation and best approximation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 4, pp. 1367-1385. doi : 10.1051/m2an/2016066. http://www.numdam.org/articles/10.1051/m2an/2016066/
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