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### Numerical computation of advection and diffusion on evolving diffuse interfaces

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Elliott, Charles M., Stinner, Björn, Styles, Vanessa and Welford, R..
(2011)
*Numerical computation of advection and diffusion on evolving diffuse interfaces.*
IMA Journal of Numerical Analysis, Vol.31
(No.3).
pp. 786-812.
ISSN 0272-4979

**Full text not available from this repository.**

Official URL: http://dx.doi.org/10.1093/imanum/drq005

## Abstract

We propose a numerical method for computing transport and diffusion on a moving surface. The approach is based on a diffuse interface model in which a bulk diffusion-advection equation is solved on a layer of thickness epsilon containing the surface. The conserved quantity in the bulk domain is the concentration weighted by a density which vanishes on the boundary of the thin domain. Such a density arises naturally in double obstacle phase field models. The discrete equations are then formulated on a moving narrow band consisting of grid points on a fixed mesh. We show that the discrete equations are solvable subject to a natural constraint on the evolution of the discrete narrow band. Mass is conserved and the discrete solution satisfies stability bounds. Numerical experiments indicate that the method is second-order accurate in space.

[error in script] [error in script]Item Type: | Journal Article |
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |

Divisions: | Faculty of Science > Mathematics |

Library of Congress Subject Headings (LCSH): | Differential equations, Partial -- Numerical solutions -- Computer programs, Interfaces (Physical sciences) -- Mathematics , Heat equation, Finite element method, Surface active agents |

Journal or Publication Title: | IMA Journal of Numerical Analysis |

Publisher: | Oxford University Press |

ISSN: | 0272-4979 |

Date: | July 2011 |

Volume: | Vol.31 |

Number: | No.3 |

Page Range: | pp. 786-812 |

Identification Number: | 10.1093/imanum/drq005 |

Status: | Peer Reviewed |

Publication Status: | Published |

Access rights to Published version: | Restricted or Subscription Access |

Funder: | Deutsche Forschungsgemeinschaft (DFG), Engineering and Physical Sciences Research Council (EPSRC) |

Grant number: | Sti 579/1-1 2 (DFG), EP/D078334/1 (EPSRC), EP/G010404 (EPSRC) |

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URI: | http://wrap.warwick.ac.uk/id/eprint/38681 |

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