hp-FEM for three-dimensional elastic plates
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.
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