hp-FEM for three-dimensional elastic plates
Monique Dauge, Christoph Schwab · ESAIM Mathematical Modelling and Numerical Analysis · 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.