A phase field model for the electromigration of intergranular voids

摘要: We propose a degenerate Allen–Cahn/Cahn–Hilliard system coupled to quasi-static diffusion equation model the motion of intergranular voids. The can be viewed as phase field with an interfacial parameter γ . In limit → 0, models evolution voids by surface and electromigration in electrically conducting solid grain boundary. introduce finite element approximation for proposed system, show stability bounds, prove convergence, hence existence weak solution this non-linear parabolic two space dimensions. An iterative scheme solving resulting discrete at each time level is introduced analysed, some numerical experiments are presented. Appendix we discuss sharp interface above tends zero.