A linear extrapolation method for a general phase relaxation problem

Jiang, Xun

Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 7 (1996) no. 3, pp. 169-179

Résumé

This paper examines a linear extrapolation time-discretization of a \( 2D \) 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 \( \pm 1 \) for phase variable. Under a stability constraint, this scheme is shown to converge with optimal orders \( \mathcal{O} (\tau | \log \tau |^{1/2}) \) for temperature and enthalpy, and \( \mathcal{O} (\tau^{1/2} | \log \tau |^{1/2}) \) for heat flux as time-step \( \tau \downarrow 0 \).