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

Schwab, Christoph

Math. Methods Appl. Sci. 18, No. 5, 345-370 (1995).

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

Keywords:

elliptic model boundary value problem; lower-dimensional models; asymptotic rate of convergence

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