The local discontinuous Galerkin method for linearized incompressible fluid flow: A review

Bernardo Cockburn; Guido Kanschat; Dominik Schötzau

doi:10.1016/j.compfluid.2003.08.005

The local discontinuous Galerkin method for linearized incompressible fluid flow: A review

Bernardo Cockburn
, Guido Kanschat
, Dominik Schötzau

School of Mathematics

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

63 Scopus citations

Abstract

In this paper, we review the development of the so-called local discontinuous Galerkin method for linearized incompressible fluid flow. This is a stable, high-order accurate and locally conservative finite element method whose approximate solution is discontinuous across inter-element boundaries; this property renders the method ideally suited for hp-adaptivity. In the context of the Oseen problem, we present the method and discuss its stability and convergence properties. We also display numerical experiments that show that the method behaves well for a wide range of Reynolds numbers.

Original language	English (US)
Pages (from-to)	491-506
Number of pages	16
Journal	Computers and Fluids
Volume	34
Issue number	4-5 SPEC.ISS.
DOIs	https://doi.org/10.1016/j.compfluid.2003.08.005
State	Published - 2005

Bibliographical note

Funding Information:
The first author was supported in part by the National Science Foundation (Grant DMS-0107609) and by the University of Minnesota Supercomputing Institute.

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10.1016/j.compfluid.2003.08.005

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title = "The local discontinuous Galerkin method for linearized incompressible fluid flow: A review",

abstract = "In this paper, we review the development of the so-called local discontinuous Galerkin method for linearized incompressible fluid flow. This is a stable, high-order accurate and locally conservative finite element method whose approximate solution is discontinuous across inter-element boundaries; this property renders the method ideally suited for hp-adaptivity. In the context of the Oseen problem, we present the method and discuss its stability and convergence properties. We also display numerical experiments that show that the method behaves well for a wide range of Reynolds numbers.",

author = "Bernardo Cockburn and Guido Kanschat and Dominik Sch{\"o}tzau",

note = "Funding Information: The first author was supported in part by the National Science Foundation (Grant DMS-0107609) and by the University of Minnesota Supercomputing Institute. ",

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TY - JOUR

T1 - The local discontinuous Galerkin method for linearized incompressible fluid flow

T2 - A review

AU - Cockburn, Bernardo

AU - Kanschat, Guido

AU - Schötzau, Dominik

N1 - Funding Information: The first author was supported in part by the National Science Foundation (Grant DMS-0107609) and by the University of Minnesota Supercomputing Institute.

PY - 2005

Y1 - 2005

N2 - In this paper, we review the development of the so-called local discontinuous Galerkin method for linearized incompressible fluid flow. This is a stable, high-order accurate and locally conservative finite element method whose approximate solution is discontinuous across inter-element boundaries; this property renders the method ideally suited for hp-adaptivity. In the context of the Oseen problem, we present the method and discuss its stability and convergence properties. We also display numerical experiments that show that the method behaves well for a wide range of Reynolds numbers.

AB - In this paper, we review the development of the so-called local discontinuous Galerkin method for linearized incompressible fluid flow. This is a stable, high-order accurate and locally conservative finite element method whose approximate solution is discontinuous across inter-element boundaries; this property renders the method ideally suited for hp-adaptivity. In the context of the Oseen problem, we present the method and discuss its stability and convergence properties. We also display numerical experiments that show that the method behaves well for a wide range of Reynolds numbers.

UR - https://www.scopus.com/pages/publications/11144289535

UR - https://www.scopus.com/pages/publications/11144289535#tab=citedBy

U2 - 10.1016/j.compfluid.2003.08.005

DO - 10.1016/j.compfluid.2003.08.005

M3 - Article

AN - SCOPUS:11144289535

SN - 0045-7930

VL - 34

SP - 491

EP - 506

JO - Computers and Fluids

JF - Computers and Fluids

IS - 4-5 SPEC.ISS.

ER -

The local discontinuous Galerkin method for linearized incompressible fluid flow: A review

Abstract

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