Differential-difference regularization for a 2D inverse heat conduction problem

We study the differential-difference regularization for a two-dimensional inverse heat conduction problem, i.e. the heat equation is semi-discretized by a differential-difference equation, where the time derivative and a spatial second-order derivative have been replaced by the finite differences, while the other spatial second-order derivative is preserved. We analyze the properties of the discretized approximation using Fourier transform techniques. Some error estimates, which give the information about how to choose the step lengths in the discretization, show that the semi-discretized form has a 'regularized effect'. We also proved the unconditional convergence of a discretization scheme involving spatial marching.

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