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A Spectral Mimetic Least-Squares Method for Generalized Convection-Diffusion Problems

  • Rasmus O. HjortEmail author
  • Bo Gervang
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 119)

Abstract

We present a spectral mimetic least-squares method for a model convection-diffusion problem, which preserves conservation properties. The problem is solved using differential geometry where the topological part and the constitutive part have been separated. It is shown that the topological part is solved exactly independent of the order of the spectral expansion. The mimetic method incorporates the Lie derivative for the convective term, by means of Cartans homotopy formula, see for example Abraham et al. (1988) (Manifolds, Tensor Analysis, and Applications, Springer, New York). The spectral mimetic least-squares method is compared to a more classic spectral least-squares method. It is shown that both schemes lead to spectral convergence.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of EngineeringAarhus UniversityAarhus CDenmark

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