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Semi-lagrangian methods for advection of differential forms

by H. Heumann and R. Hiptmair and K. Li and J.-C. Xu

(Report number 2011-21)

Abstract
We study the discretization of linear transient transport problems for differential forms on bounded domains. The focus is on semi-Lagrangian methods that employ finite element approximation on fixed meshes combined with tracking of the flow map. They enjoy unconditional stability. We derive these methods as finite element Galerkin approach to discrete material derivatives and discuss further approximations. An a priori convergence analysis is conducted and supplemented by numerical experiments.

Keywords: Convection-dffusion problem, discrete differential forms, discrete Lie derivative, semi-Lagrangian methods

@Techreport{HHLX11_65,
  author = {H. Heumann and R. Hiptmair and K. Li and J.-C. Xu},
  title = {Semi-lagrangian methods for advection of differential forms},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2011-21},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2011/2011-21.pdf },
  year = {2011}
}

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