A practical phase field method for an elliptic surface PDE

Abstract 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 estimat...

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Bibliographic Details
Published in:IMA journal of numerical analysis 2021-07, Vol.41 (3), p.1668-1695
Main Authors: Barrett, John W, Deckelnick, Klaus, Styles, Vanessa
Format: Article
Language:English
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Summary:Abstract 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.
ISSN:0272-4979
1464-3642
DOI:10.1093/imanum/draa042