Boundary layer resolution in hierarchical plate modelling
C. William Schwab · Mathematical Methods in the Applied Sciences · 1995
Abstract The dimensional reduction of an elliptic model boundary value problem on a thin, plate‐like domain of thickness 2 d is analysed. A class of lower‐dimensional models with variable model orders in the interior and near the boundary of the plate is investigated and it is shown that for a sufficiently large model order in a O ( d ∣ln d ∣)‐neighbourhood of the edge the hierarchical models compensate for the boundary layers of the exact solution—in the sense that their asymptotic rate of convergence as d → 0 is the same as the optimal one for compatible, layer‐free solutions.