The Bassi Rebay 1 scheme is a special case of the Symmetric Interior Penalty formulation for discontinuous Galerkin discretisations with Gauss–Lobatto points

In the discontinuous Galerkin (DG) community, several formulations have been proposed to solve PDEs involving second-order spatial derivatives (e.g. elliptic problems). In this paper, we show that, when the discretisation is restricted to the usage of Gauss–Lobatto points, there are important simila...

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Bibliographic Details
Published in:Journal of computational physics 2018-06, Vol.363, p.1-10
Main Authors: Manzanero, Juan, Rueda-Ramírez, Andrés M., Rubio, Gonzalo, Ferrer, Esteban
Format: Article
Language:English
Subjects:
Computational physics
Discontinuous Galerkin
Finite element analysis
Formulations
Galerkin method
Gauss–Lobatto Legendre
Normal distribution
Parameter estimation
Partial differential equations
Poisson equation
Summation-by-parts property
Symmetry
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Summary:In the discontinuous Galerkin (DG) community, several formulations have been proposed to solve PDEs involving second-order spatial derivatives (e.g. elliptic problems). In this paper, we show that, when the discretisation is restricted to the usage of Gauss–Lobatto points, there are important similarities between two common choices: the Bassi-Rebay 1 (BR1) method, and the Symmetric Interior Penalty (SIP) formulation. This equivalence enables the extrapolation of properties from one scheme to the other: a sharper estimation of the minimum penalty parameter for the SIP stability (compared to the more general estimate proposed by Shahbazi [1]), more efficient implementations of the BR1 scheme, and the compactness of the BR1 method for straight quadrilateral and hexahedral meshes.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2018.02.035