A practical phase field method for an elliptic surface PDE

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

[img] PDF - Accepted Version
Restricted to SRO admin only until 20 August 2021.

Download (719kB)

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
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: 14 Sep 2020 15:00
URI: http://sro.sussex.ac.uk/id/eprint/91584

View download statistics for this item

📧 Request an update