Standard

Residual-based variational multiscale modeling in a discontinuous Galerkin framework. / Stoter, Stein K.F.; Turteltaub, Sergio R.; Hulshoff, Steven J.; Schillinger, Dominik.

In: Multiscale Modeling and Simulation, Vol. 16, No. 3, 01.01.2018, p. 1333-1364.

Research output: Contribution to journalArticleScientificpeer-review

Harvard

Stoter, SKF, Turteltaub, SR, Hulshoff, SJ & Schillinger, D 2018, 'Residual-based variational multiscale modeling in a discontinuous Galerkin framework' Multiscale Modeling and Simulation, vol. 16, no. 3, pp. 1333-1364. https://doi.org/10.1137/17M1147044

APA

Vancouver

Author

Stoter, Stein K.F. ; Turteltaub, Sergio R. ; Hulshoff, Steven J. ; Schillinger, Dominik. / Residual-based variational multiscale modeling in a discontinuous Galerkin framework. In: Multiscale Modeling and Simulation. 2018 ; Vol. 16, No. 3. pp. 1333-1364.

BibTeX

@article{b4fccf77cd614434995967670a39df38,
title = "Residual-based variational multiscale modeling in a discontinuous Galerkin framework",
abstract = "We develop the general form of the variational multiscale method in a discontinuous Galerkin framework. Our method is based on the decomposition of the true solution into discontinuous coarse-scale and discontinuous fine-scale parts. The obtained coarse-scale weak formulation includes two types of fine-scale contributions. The first type corresponds to a fine-scale volumetric term, which we formulate in terms of a residual-based model that also takes into account fine-scale effects at element interfaces. The second type consists of independent fine-scale terms at element interfaces, which we formulate in terms of a new fine-scale {"}interface model.{"} We demonstrate for the one-dimensional Poisson problem that existing discontinuous Galerkin formulations, such as the interior penalty method, can be rederived by choosing particular fine-scale interface models. The multiscale formulation thus opens the door for a new perspective on discontinuous Galerkin methods and their numerical properties. This is demonstrated for the one-dimensional advection-diffusion problem, where we show that upwind numerical fluxes can be interpreted as an ad hoc remedy for missing volumetric fine-scale terms.",
keywords = "Multiscale discontinuous Galerkin methods, Residual-based multiscale modeling, Upwinding, Variational multiscale method",
author = "Stoter, {Stein K.F.} and Turteltaub, {Sergio R.} and Hulshoff, {Steven J.} and Dominik Schillinger",
note = "Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.",
year = "2018",
month = "1",
day = "1",
doi = "10.1137/17M1147044",
language = "English",
volume = "16",
pages = "1333--1364",
journal = "Multiscale Modeling and Simulation",
issn = "1540-3459",
publisher = "Society for Industrial and Applied Mathematics",
number = "3",

}

RIS

TY - JOUR

T1 - Residual-based variational multiscale modeling in a discontinuous Galerkin framework

AU - Stoter, Stein K.F.

AU - Turteltaub, Sergio R.

AU - Hulshoff, Steven J.

AU - Schillinger, Dominik

N1 - Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - We develop the general form of the variational multiscale method in a discontinuous Galerkin framework. Our method is based on the decomposition of the true solution into discontinuous coarse-scale and discontinuous fine-scale parts. The obtained coarse-scale weak formulation includes two types of fine-scale contributions. The first type corresponds to a fine-scale volumetric term, which we formulate in terms of a residual-based model that also takes into account fine-scale effects at element interfaces. The second type consists of independent fine-scale terms at element interfaces, which we formulate in terms of a new fine-scale "interface model." We demonstrate for the one-dimensional Poisson problem that existing discontinuous Galerkin formulations, such as the interior penalty method, can be rederived by choosing particular fine-scale interface models. The multiscale formulation thus opens the door for a new perspective on discontinuous Galerkin methods and their numerical properties. This is demonstrated for the one-dimensional advection-diffusion problem, where we show that upwind numerical fluxes can be interpreted as an ad hoc remedy for missing volumetric fine-scale terms.

AB - We develop the general form of the variational multiscale method in a discontinuous Galerkin framework. Our method is based on the decomposition of the true solution into discontinuous coarse-scale and discontinuous fine-scale parts. The obtained coarse-scale weak formulation includes two types of fine-scale contributions. The first type corresponds to a fine-scale volumetric term, which we formulate in terms of a residual-based model that also takes into account fine-scale effects at element interfaces. The second type consists of independent fine-scale terms at element interfaces, which we formulate in terms of a new fine-scale "interface model." We demonstrate for the one-dimensional Poisson problem that existing discontinuous Galerkin formulations, such as the interior penalty method, can be rederived by choosing particular fine-scale interface models. The multiscale formulation thus opens the door for a new perspective on discontinuous Galerkin methods and their numerical properties. This is demonstrated for the one-dimensional advection-diffusion problem, where we show that upwind numerical fluxes can be interpreted as an ad hoc remedy for missing volumetric fine-scale terms.

KW - Multiscale discontinuous Galerkin methods

KW - Residual-based multiscale modeling

KW - Upwinding

KW - Variational multiscale method

UR - http://www.scopus.com/inward/record.url?scp=85053021055&partnerID=8YFLogxK

U2 - 10.1137/17M1147044

DO - 10.1137/17M1147044

M3 - Article

VL - 16

SP - 1333

EP - 1364

JO - Multiscale Modeling and Simulation

T2 - Multiscale Modeling and Simulation

JF - Multiscale Modeling and Simulation

SN - 1540-3459

IS - 3

ER -

ID: 47063169