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Journal of Scientific Computing

, Volume 78, Issue 3, pp 1305–1328 | Cite as

Analysis of Discontinuous Galerkin Methods with Upwind-Biased Fluxes for One Dimensional Linear Hyperbolic Equations with Degenerate Variable Coefficients

  • Jia Li
  • Dazhi Zhang
  • Xiong MengEmail author
  • Boying Wu
Article
  • 64 Downloads

Abstract

In this paper, we analyze the discontinuous Galerkin method with upwind-biased numerical fluxes for one dimensional linear hyperbolic equations with degenerate variable coefficients. The \(L^2\)-stability is obtained by the choice of upwind-biased fluxes which could provide more flexible numerical viscosity. Furthermore, we construct some new piecewise global projections and present proofs of unique existence and optimal approximation properties. Then the optimal error estimates are derived by the benefits of the specially designed projections, essentially following the energy analysis. Numerical experiments are given which confirm the sharpness of the theoretical results.

Keywords

Discontinuous Galerkin method Upwind-biased fluxes Linear variable coefficient hyperbolic equation Error estimates 

Mathematics Subject Classification

65M60 65M12 65M15 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsHarbin Institute of TechnologyHarbinChina
  2. 2.Department of Mathematics and Institute for Advanced Study in MathematicsHarbin Institute of TechnologyHarbinChina

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