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An efficient and energy stable scheme for a phase‐field model for the moving contact line problem

In this paper, we propose for the first time a linearly coupled, energy stable scheme for the Navier–Stokes–Cahn–Hilliard system with generalized Navier boundary condition. We rigorously prove the unconditional energy stability for the proposed time discretization as well as for a fully discrete finite element scheme. Using numerical tests, we verify the accuracy, confirm the decreasing property of the discrete energy, and demonstrate the effectiveness of our method through numerical simulations in both 2‐D and 3‐D. Copyright © 2015 John Wiley & Sons, Ltd.