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A practical phase field method for an elliptic surface PDE

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posted on 2023-06-07, 07:10 authored by John W Barrett, Klaus Deckelnick, Vanessa StylesVanessa Styles
We consider a diffuse interface approach for solving an elliptic PDE on a given closed hypersurface. The method is based on a (bulk) finite element scheme employing numerical quadrature for the phase field function and hence is very easy to implement compared to other approaches. We estimate the error in natural norms in terms of the spatial grid size, the interface width and the order of the underlying quadrature rule. Numerical test calculations are presented, which confirm the form of the error bounds.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

IMA Journal of Numerical Analysis

ISSN

0272-4979

Publisher

Oxford University Press

Pages

26.0

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2020-06-04

First Open Access (FOA) Date

2021-08-20

First Compliant Deposit (FCD) Date

2020-06-03

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