# hp-FEM for three-dimensional elastic plates

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

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## Abstract

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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 ε tends to zero, the hp-discretization is consistent with the three-dimensional solution to any power of ε 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.

## 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 36.4 (2010): 597-630. <http://eudml.org/doc/194118>.

@article{Dauge2010,
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 ε tends to zero, the hp-discretization is consistent with the three-dimensional solution to any power of ε in the energy norm for the degree $p=\{\cal O\}(\left|\{\log \varepsilon\}\right|)$ and with $\{\cal O\}(\{p^4\})$ degrees of freedom. },
author = {Dauge, Monique, Schwab, Christoph},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Plates; hp-finite elements; exponential convergence; asymptotic expansion.; two-scale asymptotic expansion; energy norm},
language = {eng},
month = {3},
number = {4},
pages = {597-630},
publisher = {EDP Sciences},
title = {hp-FEM for three-dimensional elastic plates},
url = {http://eudml.org/doc/194118},
volume = {36},
year = {2010},
}

TY - JOUR
AU - Dauge, Monique
AU - Schwab, Christoph
TI - hp-FEM for three-dimensional elastic plates
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
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 ε tends to zero, the hp-discretization is consistent with the three-dimensional solution to any power of ε in the energy norm for the degree $p={\cal O}(\left|{\log \varepsilon}\right|)$ and with ${\cal O}({p^4})$ 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/194118
ER -

## References

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