paper

Tutorial on Hybridizable Discontinuous Galerkin (HDG) Formulation for Incompressible Flow Problems

arXiv:1911.05198 · doi:10.1007/978-3-030-37518-8_5

Abstract

A hybridizable discontinuous Galerkin (HDG) formulation of the linearized incompressible Navier-Stokes equations, known as Oseen equations, is presented. The Cauchy stress formulation is considered and the symmetry of the stress tensor and the mixed variable, namely the scaled strain-rate tensor, is enforced pointwise via Voigt notation. Using equal-order polynomial approximations of degree k for all variables, HDG provides a stable discretization. Moreover, owing to Voigt notation, optimal convergence of order k+1 is obtained for velocity, pressure and strain-rate tensor and a local postprocessing strategy is devised to construct an approximation of the velocity superconverging with order k+2, even for low-order polynomial approximations. A tutorial for the numerical solution of incompressible flow problems using HDG is presented, with special emphasis on the technical details required for its implementation.

35 pages, 13 figures

References in corpus (5)

Cited by in corpus (9)