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IMA Journal of Numerical Analysis 2001 21(1):81-105; doi:10.1093/imanum/21.1.81
© 2001 by Institute of Mathematics and its Applications
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Computable error bounds for some simple dimensionally reduced models on thin domains

Mark Ainsworth1 and Mark Arnold2

1 Mathematics Department, Strathclyde University, Livingstone Tower, 26 Richmond St., Glasgow, G1 1XH, UK 2 Epidemiology Department, Veterinary Laboratories Agency, New Haw, Addlestone, Surrey, KT15 3NB, UK

An approach is presented for deriving computable bounds on the error incurred in approximating an elliptic boundary value problem posed on a thin domain of laminated construction by a dimensionally reduced elliptic boundary value problem posed on the mid-surface. The theory includes cases where the domain is described in Cartesian or polar coordinates. Explicit upper bounds on the error are presented for flat plates, circular arches and spherical shells. The tightness of the bounds is illustrated by comparison with the true error for some representative examples.

Received 6 April 1999. Accepted 15 November 1999.


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