TY - JOUR
T1 - Proof of unconditional stability for a single-field discontinuous Galerkin finite element formulation for linear elasto-dynamics
AU - Costanzo, F.
AU - Huang, H.
N1 - Funding Information:
Partial support from the Air Force Office of Scientific Research through Grant No. F49620-02-1-0318 is gratefully acknowledged.
Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2005/5/20
Y1 - 2005/5/20
N2 - A discontinuous Galerkin (DG) finite element method (FEM) for the solution of linear elasto-dynamic problems is revisited and modified. The new DG FEM is based on a method originally proposed by [Comput. Methods Appl. Mech. Engrg. 84 (1990) 327] and recently adapted by [Comput. Methods Appl. Mech. Engrg. 191(46) (2002) 5315] for the solution of dynamic solid-solid phase transitions. As the FEM formulations in both the cited works have been found not to be unconditionally stable in cases where the underlying FEM grid is completely unstructured, this paper offers a modification of these formulations yielding a single-field DG FEM that is unconditionally stable without any restrictions on the grid structure. Furthermore, an energy conserving variant of the formulation is also suggested.
AB - A discontinuous Galerkin (DG) finite element method (FEM) for the solution of linear elasto-dynamic problems is revisited and modified. The new DG FEM is based on a method originally proposed by [Comput. Methods Appl. Mech. Engrg. 84 (1990) 327] and recently adapted by [Comput. Methods Appl. Mech. Engrg. 191(46) (2002) 5315] for the solution of dynamic solid-solid phase transitions. As the FEM formulations in both the cited works have been found not to be unconditionally stable in cases where the underlying FEM grid is completely unstructured, this paper offers a modification of these formulations yielding a single-field DG FEM that is unconditionally stable without any restrictions on the grid structure. Furthermore, an energy conserving variant of the formulation is also suggested.
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U2 - 10.1016/j.cma.2004.07.011
DO - 10.1016/j.cma.2004.07.011
M3 - Article
AN - SCOPUS:14944369585
SN - 0374-2830
VL - 194
SP - 2059
EP - 2076
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
IS - 18-20
ER -