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.
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e-mail: noels@mit.edu, l.noels@ulg.ac.be
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September 2007
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Alternative Approaches for the Derivation of Discontinuous Galerkin Methods for Nonlinear Mechanics
L. Noels,
L. Noels
Department of Aeronautics and Astronautics,
e-mail: noels@mit.edu, l.noels@ulg.ac.be
Massachusetts Institute of Technology
, 77 Massachusetts Ave., Cambridge, MA 02139-4307; LTAS-Milieux Continus & Thermomécanique, University of Liège
, Chemin des Chevreuils 1, B-4000 Liège, Belgium
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R. Radovitzky
R. Radovitzky
Department of Aeronautics and Astronautics,
e-mail: rapa@mit.edu
Massachusetts Institute of Technology
, 77 Massachusetts Ave., Cambridge, MA 02139-4307
Search for other works by this author on:
L. Noels
Department of Aeronautics and Astronautics,
Massachusetts Institute of Technology
, 77 Massachusetts Ave., Cambridge, MA 02139-4307; LTAS-Milieux Continus & Thermomécanique, University of Liège
, Chemin des Chevreuils 1, B-4000 Liège, Belgiume-mail: noels@mit.edu, l.noels@ulg.ac.be
R. Radovitzky
Department of Aeronautics and Astronautics,
Massachusetts Institute of Technology
, 77 Massachusetts Ave., Cambridge, MA 02139-4307e-mail: rapa@mit.edu
J. Appl. Mech. Sep 2007, 74(5): 1031-1036 (6 pages)
Published Online: July 17, 2006
Article history
Received:
June 28, 2006
Revised:
July 17, 2006
Citation
Noels, L., and Radovitzky, R. (July 17, 2006). "Alternative Approaches for the Derivation of Discontinuous Galerkin Methods for Nonlinear Mechanics." ASME. J. Appl. Mech. September 2007; 74(5): 1031–1036. https://doi.org/10.1115/1.2712228
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