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Title of Journal: Numer Math

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Abbravation: Numerische Mathematik

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Springer-Verlag

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DOI

10.1016/0923-0467(95)85014-7

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0945-3245

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A lockingfree hp DPG method for linear elasti

Authors: Jamie Bramwell Leszek Demkowicz Jay Gopalakrishnan Weifeng Qiu
Publish Date: 2012/06/26
Volume: 122, Issue: 4, Pages: 671-707
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Abstract

We present two new methods for linear elasticity that simultaneously yield stress and displacement approximations of optimal accuracy in both the mesh size h and polynomial degree p This is achieved within the recently developed discontinuous Petrov–Galerkin DPG framework In this framework both the stress and the displacement approximations are discontinuous across element interfaces We study lockingfree convergence properties and the interrelationships between the two DPG methodsWe consider a mixed method for linear elasticity with weakly imposed stress symmetry The method we consider differs from a standard method 4 only in that it has an extra Lagrange multiplier It is well known that the mixed formulation does not lock see eg 7 8 32 for homogeneous isotropic material parameters In this appendix we will provide a stability result for slightly more general materials Note however that the main goal of this appendix is to establish stability estimates for the mixed method in the form needed for the analysis of the DPG scheme in the earlier sections

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