  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.
