Numerical analysis of an isotropic phase-field model with magnetic-field effect (Q2338973)

The aim of this paper is to provide a numerical scheme based on FEM, and a numerical error and stability analysis for the model proposed by the first author and \textit{A. Belmiloudi} [J. Math. Anal. Appl. 390, No. 1, 244--273 (2012; Zbl 1387.80004)] and by \textit{A. Rasheed} et al. [Discrete Contin. Dyn. Syst. 2011, Suppl., 1224--1233 (2011; Zbl 1306.82018)] in an isotropic and isothermal regime. The semidiscrete weak form yields the differential-algebraic system which is fully discretized first by invoking Euler's backward difference method and then resolved by using the Newton iteration technique.