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

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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

Fausto Cavalli ^1, and Giovanni Naldi ^2,

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

Abstract
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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.

Keywords: Cahn-Hilliard equation; pseudo-inverse function; stable numerical methods for fourth order equations..

Mathematics Subject Classification: Primary: 65M06, 65M12; Secondary: 35Q7.

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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