Mimetic Spectral Element Advection

  • Artur PalhaEmail author
  • Pedro Pinto Rebelo
  • Marc Gerritsma
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 95)


We present a discretization of the linear advection of differential forms on bounded domains. The framework established in [4] is extended to incorporate the Lie derivative, \(\mathcal{L}\), by means of Cartan’s homotopy formula. The method is based on a physics-compatible discretization with spectral accuracy. It will be shown that the derived scheme has spectral convergence with local mass conservation. Artificial dispersion depends on the order of time integration.


Spectral Element Exterior Derivative Advection Equation Wedge Product Tangent Vector Field 
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The authors would like to thank the valuable comments of both reviewers and the funding received by FCT – Foundation for science and technology Portugal through SRF/BD/36093/2007 and SFRH/BD/79866/2011.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Artur Palha
    • 1
    Email author
  • Pedro Pinto Rebelo
    • 1
  • Marc Gerritsma
    • 1
  1. 1.Faculty of Aerospace Engineering, Aerodynamics GroupDelft University of TechnologyDelftThe Netherlands

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