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Abstract

In this paper we discuss the application of the certified reduced basis method and the associated software package rbMIT (c) to ``worked problems'' in steady and unsteady conduction. Each worked problem is characterized by an input parameter vector --- material properties, boundary conditions and sources, and geometry --- and desired outputs --- selected fluxes and temperatures. The methodology and associated rbMIT(c) software, as well as the educational worked problem framework, consists of two distinct stages: an Offline (or ``Instructor'') stage in which a new heat transfer worked problem is first created; and an Online (or ``Lecturer''/``Student'') stage in which the worked problem is subsequently invoked in (say) various in--class, project, or homework settings. In the very inexpensive Online stage, given an input parameter value, the software returns both (i) an accurate reduced basis output prediction, and (ii) a rigorous bound for the error in the reduced basis prediction relative to an underlying expensive high-fidelity finite element discretization; as required in the educational context, the response is both rapid \emph{and} reliable. We present illustrative results for two worked problems: a steady thermal fin, and unsteady thermal analysis of a delamination crack.

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