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Computable error bounds for some simple dimensionally reduced models on thin domains

Ainsworth, Mark and Arnold, Mark E. (2001) Computable error bounds for some simple dimensionally reduced models on thin domains. IMA Journal of Numerical Analysis, 21 (1). pp. 81-105. ISSN 0272-4979

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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.