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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Hjort, R.O., Gervang, B. (2017). A Spectral Mimetic Least-Squares Method for Generalized Convection-Diffusion Problems. In: Bittencourt, M., Dumont, N., Hesthaven, J. (eds) Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016. Lecture Notes in Computational Science and Engineering, vol 119. Springer, Cham. https://doi.org/10.1007/978-3-319-65870-4_21
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DOI: https://doi.org/10.1007/978-3-319-65870-4_21
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