Abstract
We consider here the two-dimensional version of the Hybrid High-Order (HHO) method for the steady incompressible Navier–Stokes equations originally introduced in [Di Pietro, Krell, A Hybrid High-Order method for the steady incompressible Navier–Stokes problem, preprint arXiv:1607.08159 math.NA]. This method displays several advantageous features: it is inf-sup stable on general meshes including polyhedral elements and nonmatching interfaces, it supports arbitrary approximation order, and has a reduced computational cost thanks to the possibility of statically condensing a subset of both velocity and pressure degrees of freedom (DOFs) at each nonlinear iteration.
The work of D.A. Di Pietro was partially supported by Agence Nationale de la Recherche project HHOMM (ANR-15-CE40-0005).
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References
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Di Pietro, D.A., Krell, S.: A hybrid high-order method for the steady incompressible navier–stokes problem (2017). arXiv:1349519v1
Acknowledgements
We are gratefully indebted to Jean-Marc Lacroix and Roland Ruelle for their help in the implementation of the code on machines of the Jean Alexandre Dieudonné laboratory (Université Côte d’Azur).
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Di Pietro, D.A., Krell, S. (2017). Benchmark Session: The 2D Hybrid High-Order Method. In: Cancès, C., Omnes, P. (eds) Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects . FVCA 2017. Springer Proceedings in Mathematics & Statistics, vol 199. Springer, Cham. https://doi.org/10.1007/978-3-319-57397-7_7
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DOI: https://doi.org/10.1007/978-3-319-57397-7_7
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