Proof of unconditional stability for a single-field discontinuous Galerkin finite element formulation for linear elasto-dynamics

F. Costanzo; H. Huang

doi:10.1016/j.cma.2004.07.011

Proof of unconditional stability for a single-field discontinuous Galerkin finite element formulation for linear elasto-dynamics

F. Costanzo, H. Huang

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	2059-2076
Number of pages	18
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	194
Issue number	18-20
DOIs	https://doi.org/10.1016/j.cma.2004.07.011
State	Published - May 20 2005

All Science Journal Classification (ASJC) codes

Computational Mechanics
Mechanics of Materials
Mechanical Engineering
Physics and Astronomy(all)
Computer Science Applications

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abstract = "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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