The Deferred Correction (DeC) methods combined with the residual distribution (RD) approach allow the construction of high order continuous Galerkin (cG) schemes avoiding the inversion of the mass matrix. With the application of entropy correction functions we can even obtain entropy conservative/dissipative spatial discretizations in this context. To handle entropy production in time, a relaxation approach has been suggested by Ketcheson. The main idea is to slightly modify the time-step size such that the approximated solution fulfills the underlying entropy conservation/dissipation constraint. In this paper, we first study the relaxation technique applied to the DeC approach as an ODE solver, then we extend this combination to the residual distribution method, requiring more technical steps. The outcome is a class of cG methods that is fully entropy conservative/dissipative and where we can still avoid the inversion of a mass matrix.
Mots clés : relaxation, entropy conservative / dissipation, deferred correction, residual distribution
@article{SMAI-JCM_2022__8__125_0,
author = {Abgrall, R\'emi and Le M\'el\'edo, \'Elise and \"Offner, Philipp and Torlo, Davide},
title = {Relaxation {Deferred} {Correction} {Methods} and their {Applications} to {Residual} {Distribution} {Schemes}},
journal = {The SMAI Journal of computational mathematics},
pages = {125--160},
publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
volume = {8},
year = {2022},
doi = {10.5802/smai-jcm.82},
language = {en},
url = {http://www.numdam.org/articles/10.5802/smai-jcm.82/}
}
TY - JOUR AU - Abgrall, Rémi AU - Le Mélédo, Élise AU - Öffner, Philipp AU - Torlo, Davide TI - Relaxation Deferred Correction Methods and their Applications to Residual Distribution Schemes JO - The SMAI Journal of computational mathematics PY - 2022 SP - 125 EP - 160 VL - 8 PB - Société de Mathématiques Appliquées et Industrielles UR - http://www.numdam.org/articles/10.5802/smai-jcm.82/ DO - 10.5802/smai-jcm.82 LA - en ID - SMAI-JCM_2022__8__125_0 ER -
%0 Journal Article %A Abgrall, Rémi %A Le Mélédo, Élise %A Öffner, Philipp %A Torlo, Davide %T Relaxation Deferred Correction Methods and their Applications to Residual Distribution Schemes %J The SMAI Journal of computational mathematics %D 2022 %P 125-160 %V 8 %I Société de Mathématiques Appliquées et Industrielles %U http://www.numdam.org/articles/10.5802/smai-jcm.82/ %R 10.5802/smai-jcm.82 %G en %F SMAI-JCM_2022__8__125_0
Abgrall, Rémi; Le Mélédo, Élise; Öffner, Philipp; Torlo, Davide. Relaxation Deferred Correction Methods and their Applications to Residual Distribution Schemes. The SMAI Journal of computational mathematics, Tome 8 (2022), pp. 125-160. doi : 10.5802/smai-jcm.82. http://www.numdam.org/articles/10.5802/smai-jcm.82/
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