Optimization methods for calibration of heat conduction models

The paper provides a summary of techniques, which are suitable for calibration of models like both stationary and nonstationary heat conduction. We assume that the PDE based models are discretized 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.