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(|log ε |) and with O(p^4) degrees of freedom.
Rennes, Zürich, October 2001.
M2AN Math. Model. Numer. Anal. 36, 4, 597--630, 2002.
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