Analysis of HDG methods for oseen equations

Aycil Cesmelioglu; Bernardo Cockburn; Ngoc Cuong Nguyen; Jaume Peraire

doi:10.1007/s10915-012-9639-y

Analysis of HDG methods for oseen equations

Aycil Cesmelioglu
, Bernardo Cockburn
, Ngoc Cuong Nguyen
, Jaume Peraire

School of Mathematics

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

48 Scopus citations

Abstract

We propose a hybridizable discontinuous Galerkin (HDG) method to numerically solve the Oseen equations which can be seen as the linearized version of the incompressible Navier-Stokes equations. We use same polynomial degree to approximate the velocity, its gradient and the pressure. With a special projection and postprocessing, we obtain optimal convergence for the velocity gradient and pressure and superconvergence for the velocity. Numerical results supporting our theoretical results are provided.

Original language	English (US)
Pages (from-to)	392-431
Number of pages	40
Journal	Journal of Scientific Computing
Volume	55
Issue number	2
DOIs	https://doi.org/10.1007/s10915-012-9639-y
State	Published - May 2013

Bibliographical note

Funding Information:
N.C. Nguyen, J. Peraire supported in part by the Singapore-MIT Alliance.

Funding Information:
B. Cockburn supported in part by the National Science Foundation (Grant DMS-0712955).

Keywords

Discontinuous Galerkin methods
Hybridizable
Oseen equations
Postprocessing
Superconvergence

Publisher link

10.1007/s10915-012-9639-y

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title = "Analysis of HDG methods for oseen equations",

abstract = "We propose a hybridizable discontinuous Galerkin (HDG) method to numerically solve the Oseen equations which can be seen as the linearized version of the incompressible Navier-Stokes equations. We use same polynomial degree to approximate the velocity, its gradient and the pressure. With a special projection and postprocessing, we obtain optimal convergence for the velocity gradient and pressure and superconvergence for the velocity. Numerical results supporting our theoretical results are provided.",

keywords = "Discontinuous Galerkin methods, Hybridizable, Oseen equations, Postprocessing, Superconvergence",

author = "Aycil Cesmelioglu and Bernardo Cockburn and Nguyen, \{Ngoc Cuong\} and Jaume Peraire",

note = "Funding Information: N.C. Nguyen, J. Peraire supported in part by the Singapore-MIT Alliance. Funding Information: B. Cockburn supported in part by the National Science Foundation (Grant DMS-0712955).",

year = "2013",

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doi = "10.1007/s10915-012-9639-y",

language = "English (US)",

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T1 - Analysis of HDG methods for oseen equations

AU - Cesmelioglu, Aycil

AU - Cockburn, Bernardo

AU - Nguyen, Ngoc Cuong

AU - Peraire, Jaume

N1 - Funding Information: N.C. Nguyen, J. Peraire supported in part by the Singapore-MIT Alliance. Funding Information: B. Cockburn supported in part by the National Science Foundation (Grant DMS-0712955).

PY - 2013/5

Y1 - 2013/5

N2 - We propose a hybridizable discontinuous Galerkin (HDG) method to numerically solve the Oseen equations which can be seen as the linearized version of the incompressible Navier-Stokes equations. We use same polynomial degree to approximate the velocity, its gradient and the pressure. With a special projection and postprocessing, we obtain optimal convergence for the velocity gradient and pressure and superconvergence for the velocity. Numerical results supporting our theoretical results are provided.

AB - We propose a hybridizable discontinuous Galerkin (HDG) method to numerically solve the Oseen equations which can be seen as the linearized version of the incompressible Navier-Stokes equations. We use same polynomial degree to approximate the velocity, its gradient and the pressure. With a special projection and postprocessing, we obtain optimal convergence for the velocity gradient and pressure and superconvergence for the velocity. Numerical results supporting our theoretical results are provided.

KW - Discontinuous Galerkin methods

KW - Hybridizable

KW - Oseen equations

KW - Postprocessing

KW - Superconvergence

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UR - https://www.scopus.com/pages/publications/84893704772#tab=citedBy

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DO - 10.1007/s10915-012-9639-y

M3 - Article

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SN - 0885-7474

VL - 55

SP - 392

EP - 431

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

IS - 2

ER -

Analysis of HDG methods for oseen equations

Abstract

Bibliographical note

Keywords

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