Istituto di Matematica Applicata e Tecnologie Informatiche     
Stefanelli U. Analysis of a variable time-step discretization for the Penrose-Fife phase relaxation problem. Preprint ercim.cnr.ian//1998-1094, 1998.
In this paper we study a fully implicit time discrete scheme with variable time-steps for a system of field equations of Penrose-Fife type governing the dynamics of phase transitions with a nonconserved order parameter. In particular, Fourier law for the heat flux and zero interfacial energy are assumed. Uniform positivity, existence and uniqueness of the discrete solution is proved, several a priori estimates are estabilished, then passage to the limit is reached via compactness and monotonicity arguments. Optimal order estimates for the discretization error are shown.
Subject Time-step discretization, Penrose-Fife relaxation problem

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