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Publication

Stability Analysis of Discontinuous Galerkin Approximations to the Elastodynamics Problem

Alfio Quarteroni
2016
Journal Articles

Abstract

We consider semi-discrete discontinuous Galerkin approximations of both displacement and displacement-stress formulations of the elastodynamics problem. We prove the stability analysis in the natural energy norm and derive optimal a-priori error estimates. For the displacement-stress formulation, schemes preserving the total energy of the system are introduced and discussed. We verify our theoretical estimates on two and three dimensions test problems.

Official source

Alfio Quarteroni
2016
Journal Articles

Abstract

Official source

Related concepts (15)

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Linear elasticity is a mathematical model of how solid objects deform and become internally stressed due to prescribed loading conditions. It is a simplification of the more general nonlinear theory of elasticity and a branch of continuum mechanics. The fundamental "linearizing" assumptions of linear elasticity are: infinitesimal strains or "small" deformations (or strains) and linear relationships between the components of stress and strain. In addition linear elasticity is valid only for stress states that do not produce yielding.

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