Free-Stream Preservation for Curved Geometrically Non-conforming Discontinuous Galerkin Spectral Elements

  • David A. KoprivaEmail author
  • Florian J. Hindenlang
  • Thomas Bolemann
  • Gregor J. Gassner


The under integration of the volume terms in the discontinuous Galerkin spectral element approximation introduces errors at non-conforming element faces that do not cancel and lead to free-stream preservation errors. We derive volume and face conditions on the geometry under which a constant state is preserved. From those, we catalog eight constraints on the geometry that preserve a constant state. Numerical examples are presented to illustrate the results.


Discontinuous Galerkin Spectral element Free-stream preservation Non-conforming 



This work was supported by a grant from the Simons Foundation (#426393, David Kopriva). G.G and T.B. have been supported by the European Research Council (ERC) under the European Union’s Eights Framework Program Horizon 2020 with the research project Extreme, ERC grant agreement no. 714487. DAK would like to thank Mr. Andres Rueda for his helpful comments during the preparation of this paper.


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Authors and Affiliations

  1. 1.Department of MathematicsThe Florida State UniversityTallahasseeUSA
  2. 2.Max Planck Institute for Plasma PhysicsGarchingGermany
  3. 3.Institute for Aerodynamics and Gas DynamicsUniversity of StuttgartStuttgartGermany
  4. 4.Mathematical Institute and Center for Data and Simulation ScienceUniversity of CologneCologneGermany

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