The Unfitted HHO Method for the Stokes Problem on Curved Domains

Erik Burman; Guillaume Delay; Alexandre Ern

doi:10.1007/978-3-030-55874-1_38

The Unfitted HHO Method for the Stokes Problem on Curved Domains

Erik Burman
, Guillaume Delay
, Alexandre Ern

University College London
Sorbonne Université
École des ponts
INRIA Institut National de Recherche en Informatique et en Automatique

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

Abstract

We design a hybrid high-order (HHO) method to approximate the Stokes problem on curved domains using unfitted meshes. We prove inf-sup stability and a priori estimates with optimal convergence rates. Moreover, we provide numerical simulations that corroborate the theoretical convergence rates. A cell-agglomeration procedure is used to prevent the appearance of small cut cells.

Original language	English
Title of host publication	Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference
Editors	Fred J. Vermolen, Cornelis Vuik
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	389-397
Number of pages	9
ISBN (Print)	9783030558734
DOIs	https://doi.org/10.1007/978-3-030-55874-1_38
Publication status	Published - 1 Jan 2021
Event	European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019 - Egmond aan Zee, Netherlands Duration: 30 Sept 2019 → 4 Oct 2019

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	139
ISSN (Print)	1439-7358
ISSN (Electronic)	2197-7100

Conference

Conference	European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019
Country/Territory	Netherlands
City	Egmond aan Zee
Period	30/09/19 → 4/10/19

Access to Document

10.1007/978-3-030-55874-1_38

Cite this

Burman, E., Delay, G., & Ern, A. (2021). The Unfitted HHO Method for the Stokes Problem on Curved Domains. In F. J. Vermolen, & C. Vuik (Eds.), Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference (pp. 389-397). (Lecture Notes in Computational Science and Engineering; Vol. 139). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-55874-1_38

Burman, Erik ; Delay, Guillaume ; Ern, Alexandre. / The Unfitted HHO Method for the Stokes Problem on Curved Domains. Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference. editor / Fred J. Vermolen ; Cornelis Vuik. Springer Science and Business Media Deutschland GmbH, 2021. pp. 389-397 (Lecture Notes in Computational Science and Engineering).

@inproceedings{c455f75043ff4352bc68dfda02687271,

title = "The Unfitted HHO Method for the Stokes Problem on Curved Domains",

abstract = "We design a hybrid high-order (HHO) method to approximate the Stokes problem on curved domains using unfitted meshes. We prove inf-sup stability and a priori estimates with optimal convergence rates. Moreover, we provide numerical simulations that corroborate the theoretical convergence rates. A cell-agglomeration procedure is used to prevent the appearance of small cut cells.",

author = "Erik Burman and Guillaume Delay and Alexandre Ern",

note = "Publisher Copyright: {\textcopyright} 2021, Springer Nature Switzerland AG.; European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019 ; Conference date: 30-09-2019 Through 04-10-2019",

year = "2021",

month = jan,

day = "1",

doi = "10.1007/978-3-030-55874-1\_38",

language = "English",

isbn = "9783030558734",

series = "Lecture Notes in Computational Science and Engineering",

publisher = "Springer Science and Business Media Deutschland GmbH",

pages = "389--397",

editor = "Vermolen, \{Fred J.\} and Cornelis Vuik",

booktitle = "Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference",

}

Burman, E, Delay, G & Ern, A 2021, The Unfitted HHO Method for the Stokes Problem on Curved Domains. in FJ Vermolen & C Vuik (eds), Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference. Lecture Notes in Computational Science and Engineering, vol. 139, Springer Science and Business Media Deutschland GmbH, pp. 389-397, European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019, Egmond aan Zee, Netherlands, 30/09/19. https://doi.org/10.1007/978-3-030-55874-1_38

The Unfitted HHO Method for the Stokes Problem on Curved Domains. / Burman, Erik; Delay, Guillaume; Ern, Alexandre.
Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference. ed. / Fred J. Vermolen; Cornelis Vuik. Springer Science and Business Media Deutschland GmbH, 2021. p. 389-397 (Lecture Notes in Computational Science and Engineering; Vol. 139).

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

TY - GEN

T1 - The Unfitted HHO Method for the Stokes Problem on Curved Domains

AU - Burman, Erik

AU - Delay, Guillaume

AU - Ern, Alexandre

PY - 2021/1/1

Y1 - 2021/1/1

N2 - We design a hybrid high-order (HHO) method to approximate the Stokes problem on curved domains using unfitted meshes. We prove inf-sup stability and a priori estimates with optimal convergence rates. Moreover, we provide numerical simulations that corroborate the theoretical convergence rates. A cell-agglomeration procedure is used to prevent the appearance of small cut cells.

AB - We design a hybrid high-order (HHO) method to approximate the Stokes problem on curved domains using unfitted meshes. We prove inf-sup stability and a priori estimates with optimal convergence rates. Moreover, we provide numerical simulations that corroborate the theoretical convergence rates. A cell-agglomeration procedure is used to prevent the appearance of small cut cells.

UR - https://www.scopus.com/pages/publications/85106409544

U2 - 10.1007/978-3-030-55874-1_38

DO - 10.1007/978-3-030-55874-1_38

M3 - Conference contribution

AN - SCOPUS:85106409544

SN - 9783030558734

T3 - Lecture Notes in Computational Science and Engineering

SP - 389

EP - 397

BT - Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference

A2 - Vermolen, Fred J.

A2 - Vuik, Cornelis

PB - Springer Science and Business Media Deutschland GmbH

T2 - European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019

Y2 - 30 September 2019 through 4 October 2019

ER -

Burman E, Delay G, Ern A. The Unfitted HHO Method for the Stokes Problem on Curved Domains. In Vermolen FJ, Vuik C, editors, Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference. Springer Science and Business Media Deutschland GmbH. 2021. p. 389-397. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-030-55874-1_38

The Unfitted HHO Method for the Stokes Problem on Curved Domains

Abstract

Publication series

Conference

Access to Document

Other files and links

Fingerprint

Cite this