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Volume 11, Issue 4
A Review of Residual Distribution Schemes for Hyperbolic and Parabolic Problems: The July 2010 State of the Art

Remi Abgrall

DOI: 10.4208/cicp.270710.130711s

Commun. Comput. Phys., 11 (2012), pp. 1043-1080.

Published online: 2012-04

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  • Abstract

We 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. 

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@Article{CiCP-11-1043, author = {Remi Abgrall}, title = {A Review of Residual Distribution Schemes for Hyperbolic and Parabolic Problems: The July 2010 State of the Art}, journal = {Communications in Computational Physics}, year = {2012}, volume = {11}, number = {4}, pages = {1043--1080}, abstract = {

We 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. 

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.270710.130711s}, url = {http://global-sci.org/intro/article_detail/cicp/7401.html} }
TY - JOUR T1 - A Review of Residual Distribution Schemes for Hyperbolic and Parabolic Problems: The July 2010 State of the Art AU - Remi Abgrall JO - Communications in Computational Physics VL - 4 SP - 1043 EP - 1080 PY - 2012 DA - 2012/04 SN - 11 DO - http://doi.org/10.4208/cicp.270710.130711s UR - https://global-sci.org/intro/article_detail/cicp/7401.html KW - AB -

We 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. 

Remi Abgrall. (2012). A Review of Residual Distribution Schemes for Hyperbolic and Parabolic Problems: The July 2010 State of the Art. Communications in Computational Physics. 11 (4). 1043-1080. doi:10.4208/cicp.270710.130711s
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