*hp*-FEM for three-dimensional elastic plates

*
Monique Dauge,
Christoph Schwab*

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.