A Variational Lagrangian Scheme for a Phase Field Model: A Discrete Energetic Variational Approach
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In this paper, we propose a variational Lagrangian scheme for a modified phase-field model, which has same equilibria states with the phase-field model of Allen-Cahn type. Our discretization is based on an energy-dissipation law in terms of the flow map. By employing a discrete energetic variational approach, this scheme preserves the variational structure of the original energy-dissipation law and is energy stable. Plentiful numerical tests show that, by choosing the initial value properly, our methods can produce the desired equilibrium and capture the thin diffuse interface with some number of mesh points.
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