An inverse finite‐element technique to determine the change of phase interface location in two‐dimensional melting problems

This paper is concerned with a two‐dimensional inverse phase change problem of particular importance to the analysis and design of welding processes. Specifically, a deforming finite‐element technique is proposed to calculate the change of phase interface location in two‐dimensional melting problems from temperature measurements at points inside the solid phase. The method is based on a minimization of the error between the measured and modelled temperatures at the sensor locations. It contains smoothing in time by utilizing future temperature data to calculate current values of the interface location as well as spatial smoothing. Several two‐dimensional examples are presented to illustrate the effectiveness of the proposed numerical model.