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2018 | OriginalPaper | Chapter

Spectral Mimetic Least-Squares Methods on Curvilinear Grids

Authors : R. O. Hjort, B. Gervang

Published in: Large-Scale Scientific Computing

Publisher: Springer International Publishing

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Abstract

We present a spectral mimetic least-squares method on curvilinear grids, which conserves important invariants. The method is developed using differential forms 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 method is applied to a model convection-diffusion problem, where we show that conservation of a potential is satisfied up to machine precision. The convective term is represented using the Lie derivative, by means of Cartans homotopy formula. The spectral mimetic least-squares method is compared to a standard spectral least-squares method. It is shown that both schemes lead to spectral convergence.

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Title: Spectral Mimetic Least-Squares Methods on Curvilinear Grids
Authors: R. O. Hjort
B. Gervang
Publisher: Springer International Publishing
Book: Large-Scale Scientific Computing
Print ISBN: 978-3-319-73440-8

Electronic ISBN: 978-3-319-73441-5

Copyright Year: 2018
DOI: https://doi.org/10.1007/978-3-319-73441-5_11

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