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Journal of Scientific Computing

, Volume 77, Issue 3, pp 1679–1702 | Cite as

A Superconvergent HDG Method for Stokes Flow with Strongly Enforced Symmetry of the Stress Tensor

  • Matteo Giacomini
  • Alexandros Karkoulias
  • Ruben Sevilla
  • Antonio Huerta
Article

Abstract

This work proposes a superconvergent hybridizable discontinuous Galerkin (HDG) method for the approximation of the Cauchy formulation of the Stokes equation using same degree of polynomials for the primal and mixed variables. The novel formulation relies on the well-known Voigt notation to strongly enforce the symmetry of the stress tensor. The proposed strategy introduces several advantages with respect to the existing HDG formulations. First, it remedies the suboptimal behavior experienced by the classical HDG method for formulations involving the symmetric part of the gradient of the primal variable. The optimal convergence of the mixed variable is retrieved and an element-by-element postprocess procedure leads to a superconvergent velocity field, even for low-order approximations. Second, no additional enrichment of the discrete spaces is required and a gain in computational efficiency follows from reducing the quantity of stored information and the size of the local problems. Eventually, the novel formulation naturally imposes physical tractions on the Neumann boundary. Numerical validation of the optimality of the method and its superconvergent properties is performed in 2D and 3D using meshes of different element types.

Keywords

Hybridizable discontinuous Galerkin Stokes flow Cauchy stress formulation Voigt notation Superconvergence 

Mathematics Subject Classification

65M60 76D07 76M10 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratori de Càlcul Numèric (LaCàN), ETS de Ingenieros de Caminos, Canales y PuertosUniversitat Politècnica de CatalunyaBarcelonaSpain
  2. 2.Centre Internacional de Metodes Numerics en Enyinyeria (CIMNE)BarcelonaSpain
  3. 3.Zienkiewicz Centre for Computational Engineering, College of EngineeringSwansea UniversityWalesUK

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