The heterogeneous multiscale method based on the discontinuous Galerkin and the finite volume methods for hyperbolic problems

Shanqin Chen; Weinan E; Chi Wang Shu

The heterogeneous multiscale method based on the discontinuous Galerkin and the finite volume methods for hyperbolic problems

Shanqin Chen, Weinan E, Chi Wang Shu

Mathematics

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

Abstract

In this paper, we review a discontinuous Galerkin (DG) method and develop a finite volume (FV) method, within the framework of the heterogeneous multiscale method (HMM), for solving hyperbolic problems. Although the methods can be applied to general cases, we consider in this paper only hyperbolic scalar advection equations and Euler systems. Error estimates are given for the linear equations and numerical results are provided for the linear and nonlinear problems to demonstrate the capability of the methods.

Original language	English (US)
Title of host publication	3rd M.I.T. Conference on Computational Fluid and Solid Mechanics
Pages	1072-1075
Number of pages	4
State	Published - 2005
Event	3rd M.I.T. Conference on Computational Fluid and Solid Mechanics - Boston, MA, United States Duration: Jun 14 2005 → Jun 17 2005

Publication series

Name	3rd M.I.T. Conference on Computational Fluid and Solid Mechanics

Other

Other	3rd M.I.T. Conference on Computational Fluid and Solid Mechanics
Country/Territory	United States
City	Boston, MA
Period	6/14/05 → 6/17/05

All Science Journal Classification (ASJC) codes

Fluid Flow and Transfer Processes
Computational Mathematics

Keywords

Advection equation
Discontinuous Galerkin method
Euler equations
Finite volume method
Heterogeneous multiscale method
Homogenization

Cite this

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title = "The heterogeneous multiscale method based on the discontinuous Galerkin and the finite volume methods for hyperbolic problems",

abstract = "In this paper, we review a discontinuous Galerkin (DG) method and develop a finite volume (FV) method, within the framework of the heterogeneous multiscale method (HMM), for solving hyperbolic problems. Although the methods can be applied to general cases, we consider in this paper only hyperbolic scalar advection equations and Euler systems. Error estimates are given for the linear equations and numerical results are provided for the linear and nonlinear problems to demonstrate the capability of the methods.",

keywords = "Advection equation, Discontinuous Galerkin method, Euler equations, Finite volume method, Heterogeneous multiscale method, Homogenization",

author = "Shanqin Chen and Weinan E and Shu, {Chi Wang}",

year = "2005",

language = "English (US)",

isbn = "0080444814",

series = "3rd M.I.T. Conference on Computational Fluid and Solid Mechanics",

pages = "1072--1075",

booktitle = "3rd M.I.T. Conference on Computational Fluid and Solid Mechanics",

note = "3rd M.I.T. Conference on Computational Fluid and Solid Mechanics ; Conference date: 14-06-2005 Through 17-06-2005",

}

Chen, S, E, W & Shu, CW 2005, The heterogeneous multiscale method based on the discontinuous Galerkin and the finite volume methods for hyperbolic problems. in 3rd M.I.T. Conference on Computational Fluid and Solid Mechanics. 3rd M.I.T. Conference on Computational Fluid and Solid Mechanics, pp. 1072-1075, 3rd M.I.T. Conference on Computational Fluid and Solid Mechanics, Boston, MA, United States, 6/14/05.

The heterogeneous multiscale method based on the discontinuous Galerkin and the finite volume methods for hyperbolic problems. / Chen, Shanqin; E, Weinan; Shu, Chi Wang.
3rd M.I.T. Conference on Computational Fluid and Solid Mechanics. 2005. p. 1072-1075 (3rd M.I.T. Conference on Computational Fluid and Solid Mechanics).

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

TY - GEN

T1 - The heterogeneous multiscale method based on the discontinuous Galerkin and the finite volume methods for hyperbolic problems

AU - Chen, Shanqin

AU - E, Weinan

AU - Shu, Chi Wang

PY - 2005

Y1 - 2005

N2 - In this paper, we review a discontinuous Galerkin (DG) method and develop a finite volume (FV) method, within the framework of the heterogeneous multiscale method (HMM), for solving hyperbolic problems. Although the methods can be applied to general cases, we consider in this paper only hyperbolic scalar advection equations and Euler systems. Error estimates are given for the linear equations and numerical results are provided for the linear and nonlinear problems to demonstrate the capability of the methods.

AB - In this paper, we review a discontinuous Galerkin (DG) method and develop a finite volume (FV) method, within the framework of the heterogeneous multiscale method (HMM), for solving hyperbolic problems. Although the methods can be applied to general cases, we consider in this paper only hyperbolic scalar advection equations and Euler systems. Error estimates are given for the linear equations and numerical results are provided for the linear and nonlinear problems to demonstrate the capability of the methods.

KW - Advection equation

KW - Discontinuous Galerkin method

KW - Euler equations

KW - Finite volume method

KW - Heterogeneous multiscale method

KW - Homogenization

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M3 - Conference contribution

AN - SCOPUS:80053439640

SN - 0080444814

SN - 9780080444819

T3 - 3rd M.I.T. Conference on Computational Fluid and Solid Mechanics

SP - 1072

EP - 1075

BT - 3rd M.I.T. Conference on Computational Fluid and Solid Mechanics

T2 - 3rd M.I.T. Conference on Computational Fluid and Solid Mechanics

Y2 - 14 June 2005 through 17 June 2005

ER -

The heterogeneous multiscale method based on the discontinuous Galerkin and the finite volume methods for hyperbolic problems

Abstract

Publication series

Other

All Science Journal Classification (ASJC) codes

Keywords

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