Analysis of parameter estimation heat conduction problems with phase change using the finite element method

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Abstract
A solution to a parameter estimation problem in heat conduction with phase change is presented. Specifically, the thermophysical properties of the material are estimated by using the temperature measurements of several sensors located inside the fixed domain.In the parameter estimation problem the error is minimized between given and modelled temperatures at sensor locations over the time interval where the experiment involved variation of the material parameters. The methods are illustrated with several examples. The effects on the solution of the locations of the sensors, the number of the sensors, the time step and the number of time steps are examined.