Journal of Scientific Computing

, Volume 72, Issue 2, pp 568–585 | Cite as

DPG Method with Optimal Test Functions for a Fractional Advection Diffusion Equation

  • Vincent J. Ervin
  • Thomas Führer
  • Norbert Heuer
  • Michael Karkulik


We develop an ultra-weak variational formulation of a fractional advection diffusion problem in one space dimension and prove its well-posedness. Based on this formulation, we define a DPG approximation with optimal test functions and show its quasi-optimal convergence. Numerical experiments confirm expected convergence properties, for uniform and adaptively refined meshes.


Fractional diffusion Riemann–Liouville fractional integral DPG method with optimal test functions Ultra-weak formulation 

Mathematics Subject Classification



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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Vincent J. Ervin
    • 1
  • Thomas Führer
    • 2
  • Norbert Heuer
    • 2
  • Michael Karkulik
    • 3
  1. 1.Department of Mathematical SciencesClemson UniversityClemsonUSA
  2. 2.Facultad de MatemáticasPontificia Universidad Católica de ChileMaculChile
  3. 3.Departamento de MatemáticaUniversidad Técnica Federico Santa MaríaValparaisoChile

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