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A High Order HDG Method for Stokes Flow in Curved Domains

  • Manuel SolanoEmail author
  • Felipe Vargas
Article
  • 37 Downloads

Abstract

We propose and analyze a high order hybridizable discontinuous Galerkin (HDG) method for the Stokes equations in a curved domain. It is based on approximating the domain by a polyhedral computational subdomain where an HDG solution is computed. To obtain a high order approximation of the Dirichlet boundary data in the computational domain, we employ a transferring technique based on integrating the approximation of the gradient. In addition, we first seek for a discrete pressure having zero-mean in the computational domain and then the zero-mean condition in the entire domain is recovered by a post-process that involves an extrapolation of the discrete pressure. We prove that the method provides optimal order of convergence for the approximations of the pressure, the velocity and its gradient, that is, order \(h^{k+1}\) if the local discrete spaces are constructed using polynomials of degree k and the meshsize is h. We present numerical experiments validating the method.

Keywords

Curved domains Unfitted methods Discontinuous Galerkin Stokes flow 

Mathematics Subject Classification

65N30 65N12 65N15 

Notes

Supplementary material

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y MatemáticasUniversidad de ConcepciónConcepciónChile
  2. 2.Centro de Investigación en Ingeniería Matemática (CI2MA)Universidad de ConcepciónConcepciónChile

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