Analysis of an HDG method for linear elasticity. (21st October 2014)

• Record Type: Journal Article
• Authors: Fu, G.; Cockburn, B.; Stolarski, H.
• Is Part Of: International journal for numerical methods in engineering. Volume 102:Number 3/4(2015)
• Page Start: 551
• Page End: 575
• Publication Date: 2014-10-21
• Subjects: discontinuous Galerkin method -- linear elasticity -- finite elements -- hybrid methods; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.4781
• Languages: English
• ISSNs: 0029-5981

Abstract

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