Errors analysis for two methods approximating the classical Caginalp’s model

Abstract

The paper concerns with the error analysis of two time-stepping schemes used in the discretization of the phase-field transition system with a classical regular potential (Caginalp’s model) and Neumann boundary conditions. Using energy methods, we establish L∞ error estimates for the implicit Euler and a fractional steps method. A numerical experiment validates the theoretical results, comparing the accuracy of the methods.