In this work, we analyze hierarchic -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 -FEM which allow to resolve the three-dimensional boundary layer profiles at robust, exponential rate. We prove that, as the plate half-thickness tends to zero, the -discretization is consistent with the three-dimensional solution to any power of in the energy norm for the degree and with degrees of freedom.
Mots-clés : 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: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {597--630},
publisher = {EDP-Sciences},
volume = {36},
number = {4},
year = {2002},
doi = {10.1051/m2an:2002027},
mrnumber = {1932306},
zbl = {1070.74046},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2002027/}
}
TY - JOUR AU - Dauge, Monique AU - Schwab, Christoph TI - $hp$-FEM for three-dimensional elastic plates JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2002 SP - 597 EP - 630 VL - 36 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2002027/ DO - 10.1051/m2an:2002027 LA - en ID - M2AN_2002__36_4_597_0 ER -
%0 Journal Article %A Dauge, Monique %A Schwab, Christoph %T $hp$-FEM for three-dimensional elastic plates %J ESAIM: Modélisation mathématique et analyse numérique %D 2002 %P 597-630 %V 36 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2002027/ %R 10.1051/m2an:2002027 %G en %F M2AN_2002__36_4_597_0
Dauge, Monique; Schwab, Christoph. $hp$-FEM for three-dimensional elastic plates. ESAIM: Modélisation mathématique et analyse numérique, Tome 36 (2002) no. 4, pp. 597-630. doi : 10.1051/m2an:2002027. http://www.numdam.org/articles/10.1051/m2an:2002027/
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