$hp$-FEM for three-dimensional elastic plates
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 36 (2002) no. 4, p. 597-630

In this work, we analyze hierarchic $hp$-finite element discretizations of the full, three-dimensional plate problem. Based on two-scale asymptotic expansion of the three-dimensional solution, we give specific mesh design principles for the $hp$-FEM which allow to resolve the three-dimensional boundary layer profiles at robust, exponential rate. We prove that, as the plate half-thickness $\epsilon$ tends to zero, the $hp$-discretization is consistent with the three-dimensional solution to any power of $\epsilon$ in the energy norm for the degree $p=𝒪\left(\left|log\epsilon \right|\right)$ and with $𝒪\left({p}^{4}\right)$ degrees of freedom.

DOI : https://doi.org/10.1051/m2an:2002027
Classification:  65N30,  74K20
Keywords: plates, hp-finite elements, exponential convergence, asymptotic expansion
@article{M2AN_2002__36_4_597_0,
author = {Dauge, Monique and Schwab, Christoph},
title = {$hp$-FEM for three-dimensional elastic plates},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {36},
number = {4},
year = {2002},
pages = {597-630},
doi = {10.1051/m2an:2002027},
zbl = {1070.74046},
mrnumber = {1932306},
language = {en},
url = {http://www.numdam.org/item/M2AN_2002__36_4_597_0}
}

Dauge, Monique; Schwab, Christoph. $hp$-FEM for three-dimensional elastic plates. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 36 (2002) no. 4, pp. 597-630. doi : 10.1051/m2an:2002027. http://www.numdam.org/item/M2AN_2002__36_4_597_0/

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