Both practice and analysis of p-FEMs and adaptive hp-FEMs raise the question what increment in the current polynomial degree p guarantees a p-independent reduction of the Galerkin error. We answer this question for the p-FEM in the simplified context of homogeneous Dirichlet problems for the Poisson equation in the two dimensional unit square with polynomial data of degree p. We show that an increment proportional to p yields a p-robust error reduction and provide computational evidence that a constant increment does not.
Mots-clés : Adaptive hp-FEM for elliptic problems, a posteriori error estimation, spectral-Galerkin approximations, saturation property
@article{M2AN_2019__53_3_987_0,
author = {Canuto, Claudio and Nochetto, Ricardo H. and Stevenson, Rob P. and Verani, Marco},
title = {A saturation property for the {spectral-Galerkin} approximation of a {Dirichlet} problem in a square},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {987--1003},
publisher = {EDP-Sciences},
volume = {53},
number = {3},
year = {2019},
doi = {10.1051/m2an/2019015},
zbl = {1426.65187},
mrnumber = {3969160},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2019015/}
}
TY - JOUR AU - Canuto, Claudio AU - Nochetto, Ricardo H. AU - Stevenson, Rob P. AU - Verani, Marco TI - A saturation property for the spectral-Galerkin approximation of a Dirichlet problem in a square JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2019 SP - 987 EP - 1003 VL - 53 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2019015/ DO - 10.1051/m2an/2019015 LA - en ID - M2AN_2019__53_3_987_0 ER -
%0 Journal Article %A Canuto, Claudio %A Nochetto, Ricardo H. %A Stevenson, Rob P. %A Verani, Marco %T A saturation property for the spectral-Galerkin approximation of a Dirichlet problem in a square %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2019 %P 987-1003 %V 53 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2019015/ %R 10.1051/m2an/2019015 %G en %F M2AN_2019__53_3_987_0
Canuto, Claudio; Nochetto, Ricardo H.; Stevenson, Rob P.; Verani, Marco. A saturation property for the spectral-Galerkin approximation of a Dirichlet problem in a square. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 53 (2019) no. 3, pp. 987-1003. doi : 10.1051/m2an/2019015. http://www.numdam.org/articles/10.1051/m2an/2019015/
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