  This article deals with a nonlocal Penrose-Fife type phase field system with
inertial term. We do not know whether we can prove existence of solutions in
reference to Colli--Grasselli--Ito [Electron. J. Differential Equations 2002,
No. 100, 32 pp.] or not (see Remark 1.1). In this paper we introduce a time
discretization scheme (see Section 2), pass to the limit as the time step $h$
goes to $0$ and obtain an error estimate for the difference between continuous
and discrete solutions (see Section 5).
