A priori error estimates of a finite‐element method for an isothermal phase‐field model related to the solidification process of a binary alloy

We introduce a piecewise linear finite‐element scheme with semi‐implicit time discretization for an evolutionary phase field system modelling the isothermal solidification process of a binary alloy. This system can be written in a vectorial form as a nonlinear parabolic system. The convergence of the scheme with error estimate is then proved by introducing a generalized vectorial elliptic projecto