A semidiscrete scheme for a Penrose-Fife system and some Stefan problems in R³

This paper is concerned with the Penrose-Fife phase-field model and some Stefan problems in which the heat flux is proportional to the gradient of the inverse absolute temperature. Recently, Colli and Sprekels proved that, as some parameters in the Penrose-Fife equations tend to zero, the corresponding solutions converge against the solutions to these Stefan problems. Following their approach, we derive a time-discrete scheme for the Penrose-Fife equations, such that analogous convergence properties hold. Furthermore, we show some error estimates and prove the existence of solutions to the scheme