Longtime behavior of a semi-implicit scheme for Caginalp phase-field model

Abstract

We present a semi-implicit scheme for the Caginalp phase-field model. The scheme is a combination of implicit Euler scheme together with Eyre’s decomposition. We prove the uniqueness of the numerical solution for small time-step and the unconditional stability of the scheme. We also show that the global attractors generated by the scheme converges to the global attractor of the continuous problem as the time step goes to zero.

Keywords

• Semi-implicit scheme
• Longtime stability
• Discrete attractor
• Two-phase flow