Barrett, John W, Deckelnick, Klaus and Styles, Vanessa (2020) A practical phase field method for an elliptic surface PDE. IMA Journal of Numerical Analysis. ISSN 0272-4979
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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.
Item Type: | Article |
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Schools and Departments: | School of Mathematical and Physical Sciences > Mathematics |
SWORD Depositor: | Mx Elements Account |
Depositing User: | Mx Elements Account |
Date Deposited: | 04 Jun 2020 08:57 |
Last Modified: | 20 Aug 2021 01:00 |
URI: | http://sro.sussex.ac.uk/id/eprint/91584 |
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