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A linear extrapolation method for a general phase relaxation problem

Xun Jiang — 1996

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

This paper examines a linear extrapolation time-discretization of a 2 D phase relaxation model with temperature dependent convection and reaction. The model consists of a diffusion-advection PDE for temperature and an ODE with double obstacle ± 1 for phase variable. Under a stability constraint, this scheme is shown to converge with optimal orders O τ log τ 1 / 2 for temperature and enthalpy, and O τ 1 / 2 log τ 1 / 2 for heat flux as time-step τ 0 .

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