Finite element approximation of a model for phase separation of a multi-component alloy with non-smooth free energy

A model for the phase separation of a multi-component alloy with non-smooth free energy is considered. An error bound is proved for a fully practical piecewise linear finite element approximation using a backward Euler time discretization. An iterative scheme for solving the resulting nonlinear algebraic system is analysed, Finally numerical experiments with three components in one and two space dimensions are presented. In the one dimensional case we compare some steady states obtained numerically with the corresponding stationary solutions of the continuous problem, which we construct explicitly.