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_13

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

Gabriel R. Barrenechea
, Michał Bosy
, Victorita Dolean

Research output: Contribution to conference › Paper › peer-review

Abstract

In several studies it has been observed that, when using stabilised ÔäÖÔéû x ÔäÖÔéû 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 ÔäÖÔéû x ÔäÖÔéû-Ôéü (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
DOIs	https://doi.org/10.1007/978-3-030-39647-3_13
Publication status	Published - Jul 2018
Event	ICOSAHOM 2018 : International Conference on Spectral and High Order Methods - London, U.K. Duration: 9 Jul 2018 → 13 Jul 2018

Conference

Conference	ICOSAHOM 2018 : International Conference on Spectral and High Order Methods
Period	9/07/18 → 13/07/18

Bibliographical note

Note: Published as: Sherwin, Spencer J., Moxey, David, Peiró, Joaquim, Vincent, Peter E. and Schwab, Christoph (2020) Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018, Cham, Switzerland : Springer-Verlag, pp. 179-189 (Lecture Notes in Computer Science volume 134). ISBN: 9783030396466, ISSN (print): 1439-7358 and ISSN (electronic) 2197-7100.

Keywords

Applied mathematics
Stokes problem
hybrid discontinuous Galerkin methods
mathematics
mathematics (all)
non standard boundary conditions
velocity

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10.1007/978-3-030-39647-3_13

Bosy-M-50087-VoRFinal published version, 314 KBLicence: CC BY

https://doi.org/10.1007/978-3-030-39647-3_13

1 Conference contribution

Stabilised hybrid discontinuous Galerkin methods for the Stokes problem with non-standard boundary conditions
Barrenechea, G. R., Bosy, M. & Dolean, V., Jul 2018, Published as: Sherwin, Spencer J., Moxey, David, Peiró, Joaquim, Vincent, Peter E. and Schwab, Christoph (2020) Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018, Cham, Switzerland : Springer-Verlag, pp. 179-189 (Lecture Notes in Computer Science volume 134). ISBN: 9783030396466, ISSN (print): 1439-7358 and ISSN (electronic) 2197-7100..
Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Cite this

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title = "Stabilised hybrid discontinuous Galerkin methods for the Stokes problem with non-standard boundary conditions",

abstract = "In several studies it has been observed that, when using stabilised {\^O}{\"a}{\"O}{\^O}{\'e}{\^u} x {\^O}{\"a}{\"O}{\^O}{\'e}{\^u} 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 {\^O}{\"a}{\"O}{\^O}{\'e}{\^u} x {\^O}{\"a}{\"O}{\^O}{\'e}{\^u}-{\^O}{\'e}{\"u} (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.",

keywords = "Applied mathematics, Stokes problem, hybrid discontinuous Galerkin methods, mathematics, mathematics (all), non standard boundary conditions, velocity",

author = "Barrenechea, \{Gabriel R.\} and Micha{\l} Bosy and Victorita Dolean",

note = "Note: Published as: Sherwin, Spencer J., Moxey, David, Peir{\'o}, Joaquim, Vincent, Peter E. and Schwab, Christoph (2020) Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018, Cham, Switzerland : Springer-Verlag, pp. 179-189 (Lecture Notes in Computer Science volume 134). ISBN: 9783030396466, ISSN (print): 1439-7358 and ISSN (electronic) 2197-7100.; ICOSAHOM 2018 : International Conference on Spectral and High Order Methods ; Conference date: 09-07-2018 Through 13-07-2018",

year = "2018",

month = jul,

doi = "10.1007/978-3-030-39647-3\_13",

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TY - CONF

T1 - Stabilised hybrid discontinuous Galerkin methods for the Stokes problem with non-standard boundary conditions

AU - Barrenechea, Gabriel R.

AU - Bosy, Michał

AU - Dolean, Victorita

N1 - Note: Published as: Sherwin, Spencer J., Moxey, David, Peiró, Joaquim, Vincent, Peter E. and Schwab, Christoph (2020) Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018, Cham, Switzerland : Springer-Verlag, pp. 179-189 (Lecture Notes in Computer Science volume 134). ISBN: 9783030396466, ISSN (print): 1439-7358 and ISSN (electronic) 2197-7100.

PY - 2018/7

Y1 - 2018/7

N2 - In several studies it has been observed that, when using stabilised ÔäÖÔéû x ÔäÖÔéû 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 ÔäÖÔéû x ÔäÖÔéû-Ôéü (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.

AB - In several studies it has been observed that, when using stabilised ÔäÖÔéû x ÔäÖÔéû 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 ÔäÖÔéû x ÔäÖÔéû-Ôéü (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.

KW - Applied mathematics

KW - Stokes problem

KW - hybrid discontinuous Galerkin methods

KW - mathematics

KW - mathematics (all)

KW - non standard boundary conditions

KW - velocity

U2 - 10.1007/978-3-030-39647-3_13

DO - 10.1007/978-3-030-39647-3_13

M3 - Paper

T2 - ICOSAHOM 2018 : International Conference on Spectral and High Order Methods

Y2 - 9 July 2018 through 13 July 2018

ER -

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

Abstract

Conference

Bibliographical note

Keywords

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Research output

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

Cite this