Finite element approximation of a phase field model arising in nanostructure patterning

We consider a fully practical finite element approximation of the nonlinear parabolic Cahn–Hilliard system γ ∂ u ∂ t − ∇ _   · ( ∇ _   w ) = 0   ,   w = − γ Δ u + γ − 1 Ψ ′ ( u ) − 1 2 α c ′ ( · , u ) | ∇ _   ϕ | 2   , ∇ _   · ( c ( · , u ) ∇ _   ϕ ) = 0   , subject to an initial condition u 0 ( . )...

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