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

Fausto Cavalli, Giovanni Naldi

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)123-142
Number of pages20
JournalKinetic and Related Models
Volume3
DOIs
Publication statusPublished - 2010

Keywords

  • Cahn-Hilliard equation
  • Pseudo-inverse function
  • Stable numerical methods for fourth order equations

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