A functional in the form of a convolution of the temperature variation in the space–time domain has been derived. It has been used as the basis for a finite element formulation of heat conduction in solids. Numerical illustrations have indicated that the space–time finite element algorithm provides a more rapid convergence to the exact solutions than the usual finite element analysis with discretization in space only.
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Tai–Ran Hsu (1985) studied this question.
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