An unfitted hybrid high-order method for the stokes interface problem

Erik Burman; Guillaume Delay; Alexandre Ern

doi:10.1093/imanum/draa059

An unfitted hybrid high-order method for the stokes interface problem

Erik Burman
, Guillaume Delay
, Alexandre Ern

Research output: Contribution to journal › Article › peer-review

Abstract

We design and analyze a hybrid high-order method on unfitted meshes to approximate the Stokes interface problem. The interface can cut through the mesh cells in a very general fashion. A cell-agglomeration procedure prevents the appearance of small cut cells. Our main results are inf-sup stability and a priori error estimates with optimal convergence rates in the energy norm. Numerical simulations corroborate these results.

Original language	English
Pages (from-to)	2362-2387
Number of pages	26
Journal	IMA Journal of Numerical Analysis
Volume	41
Issue number	4
DOIs	https://doi.org/10.1093/imanum/draa059
Publication status	Published - 1 Oct 2021

Keywords

Hybrid high-order method
Stokes interface problem
Unfitted meshes

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10.1093/imanum/draa059

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title = "An unfitted hybrid high-order method for the stokes interface problem",

abstract = "We design and analyze a hybrid high-order method on unfitted meshes to approximate the Stokes interface problem. The interface can cut through the mesh cells in a very general fashion. A cell-agglomeration procedure prevents the appearance of small cut cells. Our main results are inf-sup stability and a priori error estimates with optimal convergence rates in the energy norm. Numerical simulations corroborate these results.",

keywords = "Hybrid high-order method, Stokes interface problem, Unfitted meshes",

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AU - Burman, Erik

AU - Delay, Guillaume

AU - Ern, Alexandre

N1 - Publisher Copyright: © The Author(s) 2020.

PY - 2021/10/1

Y1 - 2021/10/1

N2 - We design and analyze a hybrid high-order method on unfitted meshes to approximate the Stokes interface problem. The interface can cut through the mesh cells in a very general fashion. A cell-agglomeration procedure prevents the appearance of small cut cells. Our main results are inf-sup stability and a priori error estimates with optimal convergence rates in the energy norm. Numerical simulations corroborate these results.

AB - We design and analyze a hybrid high-order method on unfitted meshes to approximate the Stokes interface problem. The interface can cut through the mesh cells in a very general fashion. A cell-agglomeration procedure prevents the appearance of small cut cells. Our main results are inf-sup stability and a priori error estimates with optimal convergence rates in the energy norm. Numerical simulations corroborate these results.

KW - Hybrid high-order method

KW - Stokes interface problem

KW - Unfitted meshes

UR - https://www.scopus.com/pages/publications/85119154218

U2 - 10.1093/imanum/draa059

DO - 10.1093/imanum/draa059

M3 - Article

AN - SCOPUS:85119154218

SN - 0272-4979

VL - 41

SP - 2362

EP - 2387

JO - IMA Journal of Numerical Analysis

JF - IMA Journal of Numerical Analysis

IS - 4

ER -

An unfitted hybrid high-order method for the stokes interface problem

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Keywords

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