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This work proposes a superconvergent hybridizable discontinuous Galerkin(HDG) method for the approximation of the Cauchy formulation of the Stokesequation using same degree of polynomials for the primal and mixed variables.The novel formulation relies on the well-known Voigt notation to stronglyenforce the symmetry of the stress tensor. The proposed strategy introducesseveral advantages with respect to the existing HDG formulations. First, itremedies the suboptimal behavior experienced by the classical HDG method forformulations involving the symmetric part of the gradient of the primalvariable. The optimal convergence of the mixed variable is retrieved and anelement-by-element post-process procedure leads to a superconvergent velocityfield, even for low-order approximations. Second, no additional enrichment ofthe discrete spaces is required and a gain in computational efficiency followsfrom reducing the quantity of stored information and the size of the localproblems. Eventually, the novel formulation naturally imposes physicaltractions on the Neumann boundary. Numerical validation of the optimality ofthe method and its superconvergent properties is performed in 2D and 3D usingmeshes of different element types.

A superconvergent HDG method for Stokes flow with strongly enforced symmetry of the stress tensor