## Boundary layer resolution in hierarchical plate modelling.(English)Zbl 0821.73030

Summary: The dimensional reduction of an elliptic model boundary value problem on a thin, plate-like domain of thickness $$2d$$ 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 $$d \to 0$$ is the same as the optimal one for compatible, layer-free solutions.

### MSC:

 74K20 Plates 35B25 Singular perturbations in context of PDEs
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### References:

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