The Boundary Element Method for the Solution of the Backward Heat Conduction Equation

Author： Han H.   Ingham D.B.   Yuan Y.  

Publisher： Academic Press

ISSN： 0021-9991

Source： Journal of Computational Physics, Vol.116, Iss.2, 1995-02, pp. : 292-299

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Abstract

In this paper we consider the numerical solution of the one-dimensional, unsteady heat conduction equation in which Dirichlet boundary conditions are specified at two space locations and the temperature distribution at a particular time, say T0, is given. The temperature distribution for all times, t < T0, is now required and this backward heat conduction problem is a well-known improperly posed problem. In order to solve this problem the minimal energy technique has been introduced in order to modify the boundary element method and this results in a stable approximation to the solution and the accuracy of the numerical results are very encouraging.

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