Stabilised hybrid discontinuous Galerkin methods for the Stokes problem with non-standard boundary conditions

Barrenechea, Gabriel R. and Bosy, Michał and Dolean, Victorita; Sherwin, Spencer J. and Peiró, Joaquim and Vincent, Peter E. and Moxey, David and Schwab, Christoph, eds. (2020) Stabilised hybrid discontinuous Galerkin methods for the Stokes problem with non-standard boundary conditions. In: Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018. Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018, 134 . Springer-Verlag, Cham, Switzerland, pp. 179-189. ISBN 978-3-030-39646-6 (https://doi.org/10.1007/978-3-030-39647-3)

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Abstract

In several studies it has been observed that, when using stabilised ℙk×ℙk elements for both velocity and pressure, the error for the pressure is smaller, or even of a higher order in some cases, than the one obtained when using inf-sup stable ℙk×ℙk−1 (although no formal proof of either of these facts has been given). This increase in polynomial order requires the introduction of stabilising terms, since the finite element pairs used do not guarantee the inf-sup condition. With this motivation, we apply the stabilisation approach to the hybrid discontinuous Galerkin discretisation for the Stokes problem with non-standard boundary conditions.

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