# American Institute of Mathematical Sciences

March  2010, 3(1): 123-142. doi: 10.3934/krm.2010.3.123

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

 1 Università degli Studi di Brescia, Dipartimento di Matematica, Via Valotti 9, 25133 Brescia, Italy 2 Università degli Studi di Milano, Dipartimento di Matematica "F. Enriques”, Via Saldini 50, 20133 Milano, Italy

Received  November 2009 Revised  December 2009 Published  January 2010

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.
Citation: Fausto Cavalli, Giovanni Naldi. A Wasserstein approach to the numerical solution of the one-dimensional Cahn-Hilliard equation. Kinetic & Related Models, 2010, 3 (1) : 123-142. doi: 10.3934/krm.2010.3.123
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