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Finite element approximation of a phase field model for void electromigration. (English) Zbl 1076.78012
The phenomenon of void electromigration [e.g. L. J. Cummings, G. Richardson and M. Ben Amar, Eur. J. Appl. Math. 12, 97–134 (2001; Zbl 0991.78003)] is studied here. The authors consider a fully practical finite element approximation of a certain nonlinear degenerate parabolic system $$P_\gamma$$ subject to an initial condition and flux boundary conditions. As $$\gamma$$ tends to $$0$$, this models the evolution of voids by surface diffusion in an electrically conducting solid. The aim of the paper is to propose and prove convergence of a finite element approximation of $$P_\gamma$$ and hence prove existence of a solution of $$P_\gamma$$ [cf. J. W. Barrett, S. Langdon and R. Nürnberg, Numer. Math. 96, 401–434 (2004; Zbl 1041.65076)].

##### MSC:
 78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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