Hybridized discontinuous Galerkin method for convection-diffusion problems

Issei Oikawa

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

In this paper, we propose a new hybridized discontinuous Galerkin (DG) method for the convection-diffusion problems with mixed boundary conditions. A feature of the proposed method, is that it can greatly reduce the number of globally-coupled degrees of freedom, compared with the classical DG methods. The coercivity of a convective part is achieved by adding an upwinding term. We give error estimates of optimal order in the piecewise H 1-norm for general convection-diffusion problems. Furthermore, we prove that the approximate solution given by our scheme is close to the solution of the purely convective problem when the viscosity coefficient is small. Several numerical results are presented to verify the validity of our method.

Original languageEnglish
Pages (from-to)335-354
Number of pages20
JournalJapan Journal of Industrial and Applied Mathematics
Volume31
Issue number2
DOIs
Publication statusPublished - 2014

Fingerprint

Convection-diffusion Problems
Discontinuous Galerkin Method
Galerkin methods
Upwinding
Coercivity
Mixed Boundary Conditions
Coercive force
Error Estimates
Viscosity
Approximate Solution
Degree of freedom
Boundary conditions
Verify
Norm
Numerical Results
Coefficient
Term
Convection

Keywords

  • Discontinuous Galerkin method
  • Finite element method
  • Hybridization
  • Upwind

ASJC Scopus subject areas

  • Applied Mathematics
  • Engineering(all)

Cite this

Hybridized discontinuous Galerkin method for convection-diffusion problems. / Oikawa, Issei.

In: Japan Journal of Industrial and Applied Mathematics, Vol. 31, No. 2, 2014, p. 335-354.

Research output: Contribution to journalArticle

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