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: Chapter in Book/Report/Conference proceeding › Conference contribution › 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
Title of host publication	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.
DOIs	https://doi.org/10.1007/978-3-030-39647-3_13
Publication status	Published - Jul 2018

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

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Stabilised hybrid discontinuous Galerkin methods for the Stokes problem with non-standard boundary conditions
Barrenechea, G. R., Bosy, M. & Dolean, V., Jul 2018.
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Barrenechea, G. R., Bosy, M., & Dolean, V. (2018). Stabilised hybrid discontinuous Galerkin methods for the Stokes problem with non-standard boundary conditions. In 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. https://doi.org/10.1007/978-3-030-39647-3_13

Barrenechea, Gabriel R. ; Bosy, Michał ; Dolean, Victorita. / Stabilised hybrid discontinuous Galerkin methods for the Stokes problem with non-standard boundary conditions. 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.. 2018.

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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",

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Barrenechea, GR, Bosy, M & Dolean, V 2018, Stabilised hybrid discontinuous Galerkin methods for the Stokes problem with non-standard boundary conditions. in 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.. https://doi.org/10.1007/978-3-030-39647-3_13

Stabilised hybrid discontinuous Galerkin methods for the Stokes problem with non-standard boundary conditions. / Barrenechea, Gabriel R.; Bosy, Michał; Dolean, Victorita.
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.. 2018.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

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 - Conference contribution

BT - 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.

ER -

Barrenechea GR, Bosy M, Dolean V. Stabilised hybrid discontinuous Galerkin methods for the Stokes problem with non-standard boundary conditions. In 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.. 2018 doi: 10.1007/978-3-030-39647-3_13

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

Abstract

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