Skip to main content
main-content
Top

Hint

Swipe to navigate through the articles of this issue

18-04-2015 | Issue 1/2016

Journal of Scientific Computing 1/2016

An HDG Method for Convection Diffusion Equation

Journal:
Journal of Scientific Computing > Issue 1/2016
Authors:
Weifeng Qiu, Ke Shi

Abstract

We present a new hybridizable discontinuous Galerkin (HDG) method for the convection diffusion problem on general polyhedral meshes. This new HDG method is a generalization of HDG methods for linear elasticity introduced in Qiu and Shi (2013) to problems with convection term. For arbitrary polyhedral elements, we use polynomials of degree \(k+1\) and \(k\ge 0\) to approximate the scalar variable and its gradient, respectively. In contrast, we only use polynomials of degree \(k\) to approximate the numerical trace of the scalar variable on the faces which allows for a very efficient implementation of the method, since the numerical trace of the scalar variable is the only globally coupled unknown. The global \(L^{2}\)-norm of the error of the scalar variable converges with the order of \(k+2\) while that of its gradient converges with order \(k+1\). From the point of view of degrees of freedom of the globally coupled unknown: numerical trace, this method achieves superconvergence for the scalar variable without postprocessing. A key inequality relevant to the discrete Poincaré inequality is a novel theoretical contribution. This inequality is useful to deal with convection term in this paper and is essential to error analysis of HDG methods for the Navier–Stokes equations and other nonlinear problems.

Please log in to get access to this content

To get access to this content you need the following product:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 69.000 Bücher
  • über 500 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Umwelt
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Testen Sie jetzt 30 Tage kostenlos.

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 58.000 Bücher
  • über 300 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Testen Sie jetzt 30 Tage kostenlos.

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 50.000 Bücher
  • über 380 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Umwelt
  • Maschinenbau + Werkstoffe




Testen Sie jetzt 30 Tage kostenlos.

Literature
About this article

Other articles of this Issue 1/2016

Journal of Scientific Computing 1/2016 Go to the issue

Premium Partner

    Image Credits