Analysis of an HDG method for linear elasticity

G. Fu; B. Cockburn; Henryk K Stolarski

doi:10.1002/NME.4781

Analysis of an HDG method for linear elasticity

G. Fu, B. Cockburn, Henryk K Stolarski

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30 Scopus citations

Abstract

We present the first a priori error analysis for the first hybridizable discontinuous Galerkin method for linear elasticity proposed in Internat. J. Numer. Methods Engrg. 80 (2009), no. 8, 1058–1092. We consider meshes made of polyhedral, shape-regular elements of arbitrary shape and show that, whenever piecewise-polynomial approximations of degree k ≥ 0 are used and the exact solution is smooth enough, the antisymmetric part of the gradient of the displacement converges with order k, the stress and the symmetric part of the gradient of the displacement converge with order k + 1/2, and the displacement converges with order k + 1. We also provide numerical results showing that the orders of convergence are actually sharp.

Original language	English (US)
Pages (from-to)	551-575
Number of pages	25
Journal	International Journal for Numerical Methods in Engineering
Volume	102
Issue number	3-4
DOIs	https://doi.org/10.1002/NME.4781
State	Published - Apr 2015

Bibliographical note

Funding Information:
The second author was partially supported by the National Science Foundation (DMS-1115331) and the University of Minnesota Supercomputing Institute.

Publisher Copyright:
© 2014 John Wiley & Sons, Ltd.

Keywords

discontinuous Galerkin method
finite elements
hybrid methods
linear elasticity

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10.1002/NME.4781

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title = "Analysis of an HDG method for linear elasticity",

abstract = "We present the first a priori error analysis for the first hybridizable discontinuous Galerkin method for linear elasticity proposed in Internat. J. Numer. Methods Engrg. 80 (2009), no. 8, 1058–1092. We consider meshes made of polyhedral, shape-regular elements of arbitrary shape and show that, whenever piecewise-polynomial approximations of degree k ≥ 0 are used and the exact solution is smooth enough, the antisymmetric part of the gradient of the displacement converges with order k, the stress and the symmetric part of the gradient of the displacement converge with order k + 1/2, and the displacement converges with order k + 1. We also provide numerical results showing that the orders of convergence are actually sharp.",

keywords = "discontinuous Galerkin method, finite elements, hybrid methods, linear elasticity",

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AU - Fu, G.

AU - Cockburn, B.

AU - Stolarski, Henryk K

N1 - Funding Information: The second author was partially supported by the National Science Foundation (DMS-1115331) and the University of Minnesota Supercomputing Institute. Publisher Copyright: © 2014 John Wiley & Sons, Ltd.

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N2 - We present the first a priori error analysis for the first hybridizable discontinuous Galerkin method for linear elasticity proposed in Internat. J. Numer. Methods Engrg. 80 (2009), no. 8, 1058–1092. We consider meshes made of polyhedral, shape-regular elements of arbitrary shape and show that, whenever piecewise-polynomial approximations of degree k ≥ 0 are used and the exact solution is smooth enough, the antisymmetric part of the gradient of the displacement converges with order k, the stress and the symmetric part of the gradient of the displacement converge with order k + 1/2, and the displacement converges with order k + 1. We also provide numerical results showing that the orders of convergence are actually sharp.

AB - We present the first a priori error analysis for the first hybridizable discontinuous Galerkin method for linear elasticity proposed in Internat. J. Numer. Methods Engrg. 80 (2009), no. 8, 1058–1092. We consider meshes made of polyhedral, shape-regular elements of arbitrary shape and show that, whenever piecewise-polynomial approximations of degree k ≥ 0 are used and the exact solution is smooth enough, the antisymmetric part of the gradient of the displacement converges with order k, the stress and the symmetric part of the gradient of the displacement converge with order k + 1/2, and the displacement converges with order k + 1. We also provide numerical results showing that the orders of convergence are actually sharp.

KW - discontinuous Galerkin method

KW - finite elements

KW - hybrid methods

KW - linear elasticity

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Analysis of an HDG method for linear elasticity

Abstract

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