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@article{faucris.320798155,
abstract = {We consider finite element approximations to the optimal constant for the Hardy inequality with exponent p = 2 in bounded domains of dimension n = 1 or n ≥ 3. For finite element spaces of piecewise linear and continuous functions on a mesh of size h, we prove that the approximate Hardy constant converges to the optimal Hardy constant at a rate proportional to 1/|log h|^{2}. This result holds in dimension n = 1, in any dimension n ≥ 3 if the domain is the unit ball and the finite element discretization exploits the rotational symmetry of the problem, and in dimension n = 3 for general finite element discretizations of the unit ball. In the first two cases, our estimates show excellent quantitative agreement with values of the discrete Hardy constant obtained computationally.},
author = {Pietra, Francesco Della and Fantuzzi, Giovanni and Ignat, Liviu I. and Masiello, Alba Lia and Paoli, Gloria and Zuazua, Enrique},
faupublication = {yes},
journal = {Journal of Convex Analysis},
keywords = {finite element method; Hardy constant; Hardy inequality},
note = {CRIS-Team Scopus Importer:2024-04-12},
pages = {497-523},
peerreviewed = {Yes},
title = {{Finite} {Element} {Approximation} of the {Hardy} {Constant}},
volume = {31},
year = {2024}
}