A linear extrapolation method for a general phase relaxation problem (Q1357121)

Summary: 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 \(\pm1\) 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 \(\tau\downarrow 0\).