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

An approach is presented for deriving computable bounds on the error incurr ed in approximating an elliptic boundary value problem posed on a thin doma in of laminated construction by a dimensionally reduced elliptic boundary v alue problem posed on the mid-surface. The theory includes cases where the domain is described in Cartesian or polar coordinates. Explicit upper bound s 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.