Error and stability analysis of an anisotropic phase-field model for binary-fluid mixtures in the presence of magnetic-field

In this article, we study the error and stability of the proposed numerical scheme in order to solve a two dimensional anisotropic phase-field model with convection and externally applied magnetic field in an isothermal solidification of binary alloys. The proposed numerical scheme is based on mixed finite element method satisfying the CFL condition. A particular application with real physical parameters of Nickel-Copper(Ni-Cu) is considered in order to validate the numerical scheme employed. The results of stability and error analysis substantiates complete accordance with the postulated theoretical error estimates which demonstrates the efficiency of the presented method.