The paper provides a summary of techniques, which are suitable for calibration of models like both stationary and nonstation-ary heat conduction. We assume that the PDE based models are dis-cretized by finite elements and PDE coefficients are piecewise constant on apriori given macroelements (subdomains). A special attention is given to Gauss-Newton methods, evaluation of the derivatives and application of these methods to a heat evolution problem, which arose in geoengineering.
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