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Alternative approaches for the derivation of discontinuous Galerkin methods for nonlinear mechanics
Noels, Ludovic; Radovitzky, Raúl
2007In Journal of Applied Mechanics, 74, p. 1031-1036
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Keywords :
discontinuous Galerkin; elliptic equation; hyperelasticity
Abstract :
[en] Discontinuous Galerkin methods are commonly derived by seeking a weak statement of the governing differential equations via a weighted-average approach allowing for discontinuous fields at the element interfaces of the discretization. In order to ensure consistency and stability of the formulation, this approach requires the definition of a numerical flux and a stabilization term. Discontinuous Galerkin methods may also be formulated from a linear combination of the governing and compatibility equations weighted by suitable operators. A third approach based on a variational statement of a generalized energy functional has been proposed recently for finite elasticity. This alternative approach naturally leads to an expression of the numerical flux and the stabilization terms in the context of large deformation mechanics problems. This paper compares these three approaches and establishes the conditions under which identical formulations are obtained.
Disciplines :
Mechanical engineering
Author, co-author :
Noels, Ludovic  ;  Université de Liège - ULiège > Département d'aérospatiale et mécanique > LTAS - Milieux continus et thermomécanique
Radovitzky, Raúl;  Massachusetts Institute of Technology - MIT > Aeronautics & Astronautics
Language :
English
Title :
Alternative approaches for the derivation of discontinuous Galerkin methods for nonlinear mechanics
Publication date :
2007
Journal title :
Journal of Applied Mechanics
ISSN :
0021-8936
eISSN :
1528-9036
Publisher :
American Society of Mechanical Engineers, New York, United States - New York
Volume :
74
Pages :
1031-1036
Peer reviewed :
Peer Reviewed verified by ORBi
Funders :
F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]
This research was supported by the U.S. Army through the Institute for Soldier Nanotechnologies, under Contract DAAD-19-02-D-0002 with the U.S. Army Research Office.
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