Some Remarks About Conservation for Residual Distribution Schemes

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 a...

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Bibliographic Details
Published in:Journal of computational methods in applied mathematics Vol. 18; no. 3; pp. 327 - 351
Main Author: Abgrall, Rémi
Format: Journal Article
Language:English
Published: Minsk De Gruyter 01.07.2018
Walter de Gruyter GmbH
Subjects:
65M08
76M10
Conservation
Discretization
Finite element method
Finite Element Methods
Finite volume method
Finite Volume Methods
Flux Formulation
Hyperbolic Problems
ISSN:1609-4840, 1609-9389
Online Access:Get full text
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Summary: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 [ , , , ]. This contribution is an enhanced version of [ ].
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ISSN:1609-4840
1609-9389
DOI:10.1515/cmam-2017-0056