Identification of parameters in the 2-D IHCP

We present a numerical marching scheme, based on mollification and the general cross validation methods, to determine the diffusivity coefficient, as well as the temperature and heat flux histories, in the two-dimensional inverse heat conduction problem when noisy data at the active boundary and the initial measured temperature distribution are given. No information about the quality and/or quantity of the noise is assumed. A proof of stability and convergence of the algorithm, together with several numerical examples, are provided.