$hp$-FEM for three-dimensional elastic plates

Dauge, Monique ; Schwab, Christoph

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 36 (2002), p. 597-630 / Harvested from Numdam

Résumé

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.

Détail

Publié le : 2002-01-01

MR 1932306 | Zbl 1070.74046

DOI : https://doi.org/10.1051/m2an:2002027
Classification:  65N30,  74K20

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