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Some remarks about conservation for residual distribution schemes


Abgrall, Rémi (2017). Some remarks about conservation for residual distribution schemes. Computational Methods in Applied Mathematics, 0(0):Epub ahead of print.

Abstract

We are interested in the discretisation of the steady version of hyperbolic problems. We first show that all the known schemes (up to our knowledge) can be rephrased in a common framework. Using this framework, we then show they flux formulation, with an explicit construction of the flux, and thus are locally conservative. This is well known for the finite volume schemes or the discontinuous Galerkin ones, much less known for the continuous finite element methods. We also show that Tadmor's entropy stability formulation can naturally be rephrased in this framework as an additional conservation relation discretisation, and using this, we show some connections with the recent papers [13, 20, 18, 19]. This contribution is an enhanced version of [4].

Abstract

We are interested in the discretisation of the steady version of hyperbolic problems. We first show that all the known schemes (up to our knowledge) can be rephrased in a common framework. Using this framework, we then show they flux formulation, with an explicit construction of the flux, and thus are locally conservative. This is well known for the finite volume schemes or the discontinuous Galerkin ones, much less known for the continuous finite element methods. We also show that Tadmor's entropy stability formulation can naturally be rephrased in this framework as an additional conservation relation discretisation, and using this, we show some connections with the recent papers [13, 20, 18, 19]. This contribution is an enhanced version of [4].

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2017
Deposited On:15 Jan 2018 11:33
Last Modified:24 Mar 2018 02:02
Publisher:De Gruyter
ISSN:1609-4840
OA Status:Closed
Publisher DOI:https://doi.org/10.1515/cmam-2017-0056

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Embargo till: 2018-12-06