An implicit finite element algorithm for the simulation of diffusion with phase changes in solids

A fixed grid technique is proposed for the numerical simulation of the phenomena of diffusion with phase changes in solids. This technique is based on the finite element method in space coupled with the implicit (backward) Euler algorithm in time. The examples given include the Stefan problem, heat transfer with non‐instantaneous metallurgical transformations in steels, and the simultaneous and coupled diffusion and precipitation of chemical elements during internal oxidation of steels. These examples clearly evidence the efficiency and robustness of the method developed.