scholarly journals Reinterpretation and Extension of Entropy Correction Terms for Residual Distribution and Discontinuous Galerkin Schemes: Application to Structure Preserving Discretization

2022 ◽  
pp. 110955
Author(s):  
Rémi Abgrall ◽  
Philipp Öffner ◽  
Hendrik Ranocha
Keyword(s):  
Discontinuous Galerkin ◽  
Residual Distribution ◽  
Structure Preserving ◽  
Entropy Correction ◽  
Correction Terms

scholarly journals A Review of Residual Distribution Schemes for Hyperbolic and Parabolic Problems: The July 2010 State of the Art

2012 ◽  
Vol 11 (4) ◽  
pp. 1043-1080 ◽  
Author(s):  
Remi Abgrall
Keyword(s):  
Finite Element ◽  
Discontinuous Galerkin ◽  
State Of The Art ◽  
Natural Extension ◽  
Parabolic Problems ◽  
Residual Distribution ◽  
Finite Volume Schemes ◽  
Stabilized Finite Element ◽  
Research Perspectives ◽  
Residual Distribution Schemes

AbstractWe describe and review non oscillatory residual distribution schemes that are rather natural extension of high order finite volume schemes when a special emphasis is put on the structure of the computational stencil. We provide their connections with standard stabilized finite element and discontinuous Galerkin schemes, show that their are really non oscillatory. We also discuss the extension to these methods to parabolic problems. We also draw some research perspectives.

scholarly journals A structure-preserving discontinuous Galerkin scheme for the Fisher–KPP equation

2020 ◽  
Vol 146 (1) ◽  
pp. 119-157
Author(s):  
Francesca Bonizzoni ◽  
Marcel Braukhoff ◽  
Ansgar Jüngel ◽  
Ilaria Perugia
Keyword(s):  
Discontinuous Galerkin ◽  
Kpp Equation ◽  
Galerkin Scheme ◽  
Structure Preserving ◽  
Discontinuous Galerkin Scheme

scholarly journals Some Remarks About Conservation for Residual Distribution Schemes

2018 ◽  
Vol 18 (3) ◽  
pp. 327-351 ◽  
Author(s):  
Rémi Abgrall
Keyword(s):  
Finite Element ◽  
Discontinuous Galerkin ◽  
Explicit Construction ◽  
Entropy Stability ◽  
Hyperbolic Problems ◽  
Residual Distribution ◽  
Finite Volume Schemes ◽  
Common Framework ◽  
Residual Distribution Schemes ◽  
Locally Conservative

AbstractWe 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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