Spectral mimetic least-squares methods on curvilinear grids. (English) Zbl 1476.65316
Lirkov, Ivan (ed.) et al., Large-scale scientific computing. 11th international conference, LSSC 2017, Sozopol, Bulgaria, June 5–9, 2017. Revised selected papers. Cham: Springer. Lect. Notes Comput. Sci. 10665, 111-118 (2018).
Summary: 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.
For the entire collection see [Zbl 1435.65014].
For the entire collection see [Zbl 1435.65014].
MSC:
| 65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |
References:
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