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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)].

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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