| Issue |
ESAIM: M2AN
Volume 36, Number 4, July/August 2002
|
|
|---|---|---|
| Page(s) | 597 - 630 | |
| DOI | https://doi.org/10.1051/m2an:2002027 | |
| Published online | 15 September 2002 | |
hp-FEM for three-dimensional elastic plates
1
Institut Mathématique, UMR 6625 du CNRS, Université de
Rennes 1, Campus de Beaulieu, 35042 Rennes, France. Monique.Dauge@univ-rennes1.fr.
2
Seminar für Angewandte Mathematik, ETH Zürich, ETHZ HG G58.1, CH 8092 Zürich, Switzerland.
Received:
30
October
2001
Revised:
6
March
2002
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
and with 
degrees of freedom.
Mathematics Subject Classification: 65N30 / 74K20
Key words: Plates / hp-finite elements / exponential convergence / asymptotic expansion.
© EDP Sciences, SMAI, 2002
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