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

Gabriel R. Barrenechea; Michał Bosy; Victorita Dolean

doi:10.1007/978-3-030-39647-3

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

Gabriel R. Barrenechea, Michał Bosy, Victorita Dolean

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

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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.

Original language	English
Title of host publication	Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018
Subtitle of host publication	Selected Papers from the ICOSAHOM Conference, London, UK, July 9-13, 2018
Editors	Spencer J. Sherwin, Joaquim Peiró, Peter E. Vincent, David Moxey, Christoph Schwab
Place of Publication	Cham, Switzerland
Publisher	Springer-Verlag
Pages	179-189
Number of pages	11
Volume	134
ISBN (Print)	978-3-030-39646-6
DOIs	https://doi.org/10.1007/978-3-030-39647-3
Publication status	Published - 5 Aug 2020

Publication series

Name	Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018
Publisher	Springer-Verlag

Keywords

velocity
Stokes problem
non standard boundary conditions
hybrid discontinuous Galerkin methods

Access to Document

10.1007/978-3-030-39647-3

Barrenechea-etal-2020-Stabilised-hybrid-discontinuous-Galerkin-methods-for-the-StokesAccepted author manuscript, 178 KB

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, J. Peiró, P. E. Vincent, D. Moxey, & 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, pp. 179-189). (Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018). Springer-Verlag. https://doi.org/10.1007/978-3-030-39647-3

Barrenechea, Gabriel R. ; Bosy, Michał ; Dolean, Victorita. / Stabilised hybrid discontinuous Galerkin methods for the Stokes problem with non-standard boundary conditions. Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018: Selected Papers from the ICOSAHOM Conference, London, UK, July 9-13, 2018. editor / Spencer J. Sherwin ; Joaquim Peiró ; Peter E. Vincent ; David Moxey ; Christoph Schwab. Vol. 134 Cham, Switzerland : Springer-Verlag, 2020. pp. 179-189 (Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018).

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Barrenechea, GR, Bosy, M & Dolean, V 2020, Stabilised hybrid discontinuous Galerkin methods for the Stokes problem with non-standard boundary conditions. in SJ Sherwin, J Peiró, PE Vincent, D Moxey & 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, Cham, Switzerland, pp. 179-189. https://doi.org/10.1007/978-3-030-39647-3

Stabilised hybrid discontinuous Galerkin methods for the Stokes problem with non-standard boundary conditions. / Barrenechea, Gabriel R.; Bosy, Michał; Dolean, Victorita.

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018: Selected Papers from the ICOSAHOM Conference, London, UK, July 9-13, 2018. ed. / Spencer J. Sherwin; Joaquim Peiró; Peter E. Vincent; David Moxey; Christoph Schwab. Vol. 134 Cham, Switzerland : Springer-Verlag, 2020. p. 179-189 (Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

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AB - 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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Barrenechea GR, Bosy M, Dolean V. Stabilised hybrid discontinuous Galerkin methods for the Stokes problem with non-standard boundary conditions. In Sherwin SJ, Peiró J, Vincent PE, Moxey D, Schwab C, editors, 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. Cham, Switzerland: Springer-Verlag. 2020. p. 179-189. (Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018). https://doi.org/10.1007/978-3-030-39647-3