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Time discontinuous Galerkin methods with energy decaying correction for non‐linear elastodynamics
Author(s) -
de Miranda Stefano,
Mancuso Massimo,
Ubertini Francesco
Publication year - 2010
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2826
Subject(s) - discontinuous galerkin method , dissipation , finite element method , mathematics , galerkin method , simple (philosophy) , stability (learning theory) , energy (signal processing) , mathematical optimization , computer science , physics , structural engineering , engineering , philosophy , statistics , epistemology , machine learning , thermodynamics
In this paper a new time discontinuous Galerkin (TDG) formulation for non‐linear elastodynamics is presented. The new formulation embeds an energy correction which ensures truly energy decaying, thus allowing to achieve unconditional stability that, as shown in the paper, is not guaranteed by the classical TDG formulation. The resulting method is simple and easily implementable into existing finite element codes. Moreover, it inherits the desirable higher‐order accuracy and high‐frequency dissipation properties of the classical formulation. Numerical results illustrate the very good performance of the proposed formulation. Copyright © 2010 John Wiley & Sons, Ltd.