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BIT Numerical Mathematics

, Volume 51, Issue 4, pp 809–844 | Cite as

The discontinuous Galerkin method for fractional degenerate convection-diffusion equations

  • Simone Cifani
  • Espen R. JakobsenEmail author
  • Kenneth H. Karlsen
Open Access
Article

Abstract

We propose and study discontinuous Galerkin methods for strongly degenerate convection-diffusion equations perturbed by a fractional diffusion (Lévy) operator. We prove various stability estimates along with convergence results toward properly defined (entropy) solutions of linear and nonlinear equations. Finally, the qualitative behavior of solutions of such equations are illustrated through numerical experiments.

Keywords

Convection-diffusion equations Degenerate parabolic Conservation laws Fractional diffusion Entropy solutions Direct/local discontinuous Galerkin methods 

Mathematics Subject Classification (2000)

65M60 65M12 35K59 35R11 35K65 35L67 

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Copyright information

© The Author(s) 2011

Authors and Affiliations

  • Simone Cifani
    • 1
  • Espen R. Jakobsen
    • 1
    Email author
  • Kenneth H. Karlsen
    • 2
  1. 1.Department of MathematicsNorwegian University of Science and Technology (NTNU)TrondheimNorway
  2. 2.Centre of Mathematics for Applications (CMA), Department of MathematicsUniversity of OsloOsloNorway

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