h p -FEM for three-dimensional elastic plates

Monique Dauge; Christoph Schwab

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2002)

  • Volume: 36, Issue: 4, page 597-630
  • ISSN: 0764-583X

Abstract

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In this work, we analyze hierarchic h p -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 h p -FEM which allow to resolve the three-dimensional boundary layer profiles at robust, exponential rate. We prove that, as the plate half-thickness ε tends to zero, the h p -discretization is consistent with the three-dimensional solution to any power of ε in the energy norm for the degree p = 𝒪 ( log ε ) and with 𝒪 ( p 4 ) degrees of freedom.

How to cite

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Dauge, Monique, and Schwab, Christoph. "$hp$-FEM for three-dimensional elastic plates." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 36.4 (2002): 597-630. <http://eudml.org/doc/245307>.

@article{Dauge2002,
abstract = {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 $\varepsilon $ tends to zero, the $hp$-discretization is consistent with the three-dimensional solution to any power of $\varepsilon $ in the energy norm for the degree $p=\{\mathcal \{O\}\}(\left|\{\log \varepsilon \}\right|)$ and with $\{\mathcal \{O\}\}(\{p^4\})$ degrees of freedom.},
author = {Dauge, Monique, Schwab, Christoph},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {plates; hp-finite elements; exponential convergence; asymptotic expansion; two-scale asymptotic expansion; energy norm},
language = {eng},
number = {4},
pages = {597-630},
publisher = {EDP-Sciences},
title = {$hp$-FEM for three-dimensional elastic plates},
url = {http://eudml.org/doc/245307},
volume = {36},
year = {2002},
}

TY - JOUR
AU - Dauge, Monique
AU - Schwab, Christoph
TI - $hp$-FEM for three-dimensional elastic plates
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2002
PB - EDP-Sciences
VL - 36
IS - 4
SP - 597
EP - 630
AB - 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 $\varepsilon $ tends to zero, the $hp$-discretization is consistent with the three-dimensional solution to any power of $\varepsilon $ in the energy norm for the degree $p={\mathcal {O}}(\left|{\log \varepsilon }\right|)$ and with ${\mathcal {O}}({p^4})$ degrees of freedom.
LA - eng
KW - plates; hp-finite elements; exponential convergence; asymptotic expansion; two-scale asymptotic expansion; energy norm
UR - http://eudml.org/doc/245307
ER -

References

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