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A superconvergent hybridisable discontinuous Galerkin method for linear elasticity

Rubén Sevilla Orcid Logo, Matteo Giacomini, Alexandros Karkoulias, Antonio Huerta

International Journal for Numerical Methods in Engineering, Volume: 116, Issue: 2, Pages: 91 - 116

Swansea University Author: Rubén Sevilla Orcid Logo

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DOI (Published version): 10.1002/nme.5916

Abstract

The first super‐convergent hybridisable discontinuous Galerkin (HDG) method for linear elastic problems capable of using the same degree of approximation for both the primal and mixed variables is presented. The key feature of the method is the strong imposition of the symmetry of the stress tensor...

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Published in: International Journal for Numerical Methods in Engineering
ISSN: 00295981
Published: 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa40780
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Abstract: The first super‐convergent hybridisable discontinuous Galerkin (HDG) method for linear elastic problems capable of using the same degree of approximation for both the primal and mixed variables is presented. The key feature of the method is the strong imposition of the symmetry of the stress tensor by means of the well‐known and extensively used Voigt notation, circumventing the use of complex mathematical concepts to enforce the symmetry of the stress tensor either weakly or strongly. A novel procedure to construct element‐by‐element a super‐convergent post‐processed displacement is proposed. Contrary to other HDG formulations, the methodology proposed here is able to produce a super‐convergent displacement field for low order approximations. The resulting method is robust and locking‐free in the nearly incompressible limit. An extensive set of numerical examples is utilised to provide evidence of the optimality of the method and its super‐convergent properties in two and three dimensions and for different element types.
Keywords: Hybridisable discontinuous Galerkin, Elasticity, Mixed formulation, Voigt notation, Super‐convergence, Locking‐free
College: College of Engineering
Issue: 2
Start Page: 91
End Page: 116