Analysis of a variable time-step discretization for the Penrose-Fife phase relaxation problem (Q5940154)

The paper deals with the analysis of a variable time-step discretization for the Penrose-Fife phase relaxation problem. The field equations involved are nonlinear in nature.NEWLINENEWLINENEWLINEEarlier, existence and uniqueness results for the nonlinear system have been derived by \textit{P. Colli} and \textit{J. Sprekels} [Adv. Math. Sci. Appl. 9, No. 1, 383-391 (1999; Zbl 0930.35036)] by the use of the maximum principle. Herein, the main interest is to investigate the system via a direct approach based on a suitable time discretization, and especially that of showing convergence results and error esimates related to the discrete scheme, in which the time step may vary.NEWLINENEWLINENEWLINEA proof of existence and uniqueness of the discrete solution along with its positivity is presented herein. Error estimates are also deduced. The appendix contains a technical convergence result.NEWLINENEWLINENEWLINEThe paper has interesting applications in solid-liquid phase transition.