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A high-order elliptic PDE based level set reinitialisation method using a discontinuous Galerkin discretisation.

Adams, T. and Giani, S. and Coombs, W.M. (2019) 'A high-order elliptic PDE based level set reinitialisation method using a discontinuous Galerkin discretisation.', Journal of computational physics., 379 . pp. 373-391.


In this paper, an efficient, high-order accurate, level set reinitialisation method is proposed, based on the elliptic reinitialisation method (Basting and Kuzmin, 2013 [1]), which is discretised spatially using the discontinuous Galerkin (DG) symmetric interior penalty method (SIPG). In order to achieve this a number of improvements have been made to the elliptic reinitialisation method including; reformulation of the underlying minimisation problem driving the solution; adoption of a Lagrange multiplier approach for enforcing a Dirichlet boundary condition on the implicit level set interface; and adoption of a narrow band approach. Numerical examples confirm the high-order accuracy of the resultant method by demonstrating experimental orders of convergence congruent with optimal convergence rates for the SIPG method, that is and in the and DG norms respectively. Furthermore, the degree to which the level set function satisfies the Eikonal equation improves proportionally to , and the often ignored homogeneous Dirichlet boundary condition on the interface is shown to be satisfied accurately with a rate of convergence of at least for all polynomial orders.

Item Type:Article
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Publisher statement:© 2019 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (
Date accepted:05 December 2018
Date deposited:07 December 2018
Date of first online publication:12 December 2018
Date first made open access:12 December 2019

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