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A Wasserstein approach to the numerical solution of the one-dimensional Cahn-Hilliard equation

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  • In this work we introduce a new numerical approach for solving Cahn-Hilliard equation with Neumann boundary conditions involving recent mass transportation methods. The numerical scheme is based on an alternative formulation of the problem using the so called pseudo-inverse of the cumulative distribution function. We establish a stable fully discrete scheme that inherits the energy dissipation and mass conservation from the associated continuous problem. We perform some numerical experiments which confirm our results.
    Mathematics Subject Classification: Primary: 65M06, 65M12; Secondary: 35Q70.

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