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A semi-Lagrangian method for convection of differential forms

by H. Heumann and R. Hiptmair and J. Xu

(Report number 2009-09)

Abstract
We propose a semi-Lagrangian discretization method for convection problems of differential forms. Our method approximates the material derivative using the nodal interpolation operator of discrete differential forms. Thereby the method is stable by construction. As application we derive a semi-Lagrangian discretization for the electromagnetic part of MHD equations.

Keywords:

@Techreport{HHX09_43,
  author = {H. Heumann and R. Hiptmair and J. Xu},
  title = {A semi-Lagrangian method for convection of differential forms},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2009-09},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2009/2009-09.pdf },
  year = {2009}
}

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