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Volume 5, Issue 2-4
Development of Residual Distribution Schemes for the Discontinuous Galerkin Method: The Scalar Case with Linear Elements

Rémi Abgrall & Chi-Wang Shu

Commun. Comput. Phys., 5 (2009), pp. 376-390.

Published online: 2009-02

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  • Abstract

In this paper, we reformulate the piecewise linear discontinuous Galerkin (DG) method for solving two dimensional steady state scalar conservation laws in the framework of residual distribution (RD) schemes. This allows us to propose a new class of nonlinear stabilization that does not destroy the formal accuracy of the schemes. Numerical results are shown to demonstrate the behavior of this approach. 

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@Article{CiCP-5-376, author = {Rémi Abgrall and Chi-Wang Shu}, title = {Development of Residual Distribution Schemes for the Discontinuous Galerkin Method: The Scalar Case with Linear Elements}, journal = {Communications in Computational Physics}, year = {2009}, volume = {5}, number = {2-4}, pages = {376--390}, abstract = {

In this paper, we reformulate the piecewise linear discontinuous Galerkin (DG) method for solving two dimensional steady state scalar conservation laws in the framework of residual distribution (RD) schemes. This allows us to propose a new class of nonlinear stabilization that does not destroy the formal accuracy of the schemes. Numerical results are shown to demonstrate the behavior of this approach. 

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7737.html} }
TY - JOUR T1 - Development of Residual Distribution Schemes for the Discontinuous Galerkin Method: The Scalar Case with Linear Elements AU - Rémi Abgrall & Chi-Wang Shu JO - Communications in Computational Physics VL - 2-4 SP - 376 EP - 390 PY - 2009 DA - 2009/02 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7737.html KW - AB -

In this paper, we reformulate the piecewise linear discontinuous Galerkin (DG) method for solving two dimensional steady state scalar conservation laws in the framework of residual distribution (RD) schemes. This allows us to propose a new class of nonlinear stabilization that does not destroy the formal accuracy of the schemes. Numerical results are shown to demonstrate the behavior of this approach. 

Rémi Abgrall and Chi-Wang Shu. (2009). Development of Residual Distribution Schemes for the Discontinuous Galerkin Method: The Scalar Case with Linear Elements. Communications in Computational Physics. 5 (2-4). 376-390. doi:
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