Author(s)

D. Lesnic, L. Elliott & D.B. Ingham

Abstract

Boundary element method for an improperly posed problem in unsteady heat conduction D. Lesnic, L. Elliott & D.B. Ingham Department of Applied Mathematical Studies, University of Leeds, Leeds LS2 9JT, UK Abstract In this one-dimensional, unsteady, inverse heat conduction problem (IHCP) the boundary conditions are enforced at time t = 0, at x = d (0 < d 3 1) and x = 1 and the solution is sought using the Boundary Element Method (BEM). Because this is an improperly posed problem the direct method cannot be applied and special corrective procedures, such as least squares and minimal energy methods, have been introduced. From all the numerical results performed it has been found that both the least squares and the minimal energy methods give good agreement with the analytical solutions provided that the known boundary condition is extended over a suitable additional time interval such that accurate result

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