An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy with a concentration dependent mobility matrix

Using a slightly different discretization scheme in time and adapting the a pproach in Nochetto et al, (1998) for analysing the time discretization err or in the backward Euler method, we improve on the error bounds derived in (i) Barrett and Blowey (1998) and (ii) Barrett and Blowey (1999c) for a ful ly practical piecewise linear finite element approximation of a model for p hase separation of a multi-component alloy with a concentration dependent m obility matrix and (i) a logarithmic free energy, and (ii) a non-smooth fre e energy (the deep quench limit); respectively. Moreover, the improved erro r bound in the deep quench limit is optimal. Numerical experiments with thr ee components illustrating the above error bounds are also presented.