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

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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 stability 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.
Original languageEnglish
Title of host publicationSpectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018
Subtitle of host publicationSelected Papers from the ICOSAHOM Conference, London, UK, July 9-13, 2018
EditorsSpencer J. Sherwin, David Moxey, Joaquim Peiro, Peter E. Vincent, Christoph Schwab
Place of PublicationCham, Switzerland
PublisherSpringer-Verlag
Number of pages8
Volume134
ISBN (Print)978-3-030-39646-6
DOIs
Publication statusPublished - 5 Aug 2020

Publication series

NameSpectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018
PublisherSpringer-Verlag

Keywords

  • velocity
  • Stokes problem
  • non standard boundary conditions
  • hybrid discontinuous Galerkin methods

Cite this

Barrenechea, G. R., Bosy, M., & Dolean, V. (2020). Stabilised hybrid discontinuous Galerkin methods for the Stokes problem with non-standard boundary conditions. In S. J. Sherwin, D. Moxey, J. Peiro, P. E. Vincent, & C. Schwab (Eds.), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018: Selected Papers from the ICOSAHOM Conference, London, UK, July 9-13, 2018 (Vol. 134). (Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018). Springer-Verlag. https://doi.org/10.1007/978-3-030-39647-3