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Journal of Scientific Computing

Erschienen in:

01.08.2013

The Compact Discontinuous Galerkin Method for Nearly Incompressible Linear Elasticity

verfasst von: Xuehai Huang, Jianguo Huang

Erschienen in: Journal of Scientific Computing | Ausgabe 2/2013

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Abstract

A compact discontinuous Galerkin method (CDG) is devised for nearly incompressible linear elasticity, through replacing the global lifting operator for determining the numerical trace of stress tensor in a local discontinuous Galerkin method (cf. Chen et al., Math Probl Eng 20, 2010) by the local lifting operator and removing some jumping terms. It possesses the compact stencil, that means the degrees of freedom in one element are only connected to those in the immediate neighboring elements. Optimal error estimates in broken energy norm, \(H^1\)-norm and \(L^2\)-norm are derived for the method, which are uniform with respect to the Lamé constant \(\lambda .\) Furthermore, we obtain a post-processed \(H(\text{ div})\)-conforming displacement by projecting the displacement and corresponding trace of the CDG method into the Raviart–Thomas element space, and obtain optimal error estimates of this numerical solution in \(H(\text{ div})\)-seminorm and \(L^2\)-norm, which are uniform with respect to \(\lambda .\) A series of numerical results are offered to illustrate the numerical performance of our method.

Vorheriger Artikel A Well-Balanced Reconstruction of Wet/Dry Fronts for the Shallow Water Equations

Nächster Artikel Study of conservation and recurrence of Runge–Kutta discontinuous Galerkin schemes for Vlasov–Poisson systems

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Titel: The Compact Discontinuous Galerkin Method for Nearly Incompressible Linear Elasticity
verfasst von: Xuehai Huang
Jianguo Huang
Publikationsdatum: 01.08.2013
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 2/2013
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-012-9676-6

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