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hp-FEM for three-dimensional elastic plates

Published online by Cambridge University Press:  15 September 2002

Monique Dauge  and
Christoph Schwab
Monique Dauge
Affiliation:
Institut Mathématique, UMR 6625 du CNRS, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes, France. Monique.Dauge@univ-rennes1.fr.
Christoph Schwab
Affiliation:
Seminar für Angewandte Mathematik, ETH Zürich, ETHZ HG G58.1, CH 8092 Zürich, Switzerland.
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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.

Keywords

Plateshp-finite elementsexponential convergenceasymptotic expansion.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 36 , Issue 4 , July 2002 , pp. 597 - 630
Copyright
© EDP Sciences, SMAI, 2002

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