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.
A Wasserstein approach to the numerical solution of the one-dimensional Cahn-Hilliard equation / F. Cavalli, G. Naldi. - In: KINETIC AND RELATED MODELS. - ISSN 1937-5093. - 3:1(2010), pp. 123-142.
A Wasserstein approach to the numerical solution of the one-dimensional Cahn-Hilliard equation
G. NaldiUltimo
2010
Abstract
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.Pubblicazioni consigliate
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