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Stabilized virtual element methods for the unsteady incompressible Navier–Stokes equations

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Abstract

We present a stabilized virtual element method (VEM) for the unsteady incompressible Navier–Stokes equations. In this work, the concepts of stabilized methods are introduced into the VEM formulation. Thus, the variational form is enriched with stabilization terms that enable to circumvent the Babuška–Brezzi condition and to stabilize the solution for convection dominated flows. Numerical examples are presented to show the behavior of the method.

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Notes

  1. We call this mesh “hexagonal mesh” because the majority of the elements are hexagons. However, there are also elements with other number of vertices, which are mainly located on the boundary of the domain.

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Acknowledgements

This work has been partially funded by Gobierno de Aragón and FEDER funding from the European Union (Grupo Consolidado de Mecánica de Fluidos Coputacional T21) and by the Ministerio de Economía y Competitividad under contract MAT2016-76039-C4-4-R (AEI/FEDER, UE).

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  1. Universidad de Zaragoza, C/Maria de Luna 3, 50018, Zaragoza, Spain

    Diego Irisarri & Guillermo Hauke

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  1. Diego Irisarri
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  2. Guillermo Hauke
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Correspondence to Diego Irisarri.

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Irisarri, D., Hauke, G. Stabilized virtual element methods for the unsteady incompressible Navier–Stokes equations. Calcolo 56, 38 (2019). https://doi.org/10.1007/s10092-019-0332-5

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