The heterogeneous multiscale method based on the discontinuous Galerkin method for hyperbolic and parabolic problems

Shanqin Chen; E. Weinan; Chi Wang Shu

doi:10.1137/040612622

The heterogeneous multiscale method based on the discontinuous Galerkin method for hyperbolic and parabolic problems

Shanqin Chen, E. Weinan, Chi Wang Shu

Mathematics

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

26 Scopus citations

Abstract

In this paper we develop a discontinuous Galerkin (DG) method, within the framework of the heterogeneous multiscale method (HMM), for solving hyperbolic and parabolic multiscale problems. Hyperbolic scalar equations and systems, as well as parabolic scalar problems, are considered. 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 method.

Original language	English (US)
Pages (from-to)	871-894
Number of pages	24
Journal	Multiscale Modeling and Simulation
Volume	3
Issue number	4
DOIs	https://doi.org/10.1137/040612622
State	Published - 2005

All Science Journal Classification (ASJC) codes

General Chemistry
Modeling and Simulation
Ecological Modeling
General Physics and Astronomy
Computer Science Applications

Keywords

Discontinuous Galerkin method
Heterogeneous multiscale method
Homogenization

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10.1137/040612622

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abstract = "In this paper we develop a discontinuous Galerkin (DG) method, within the framework of the heterogeneous multiscale method (HMM), for solving hyperbolic and parabolic multiscale problems. Hyperbolic scalar equations and systems, as well as parabolic scalar problems, are considered. 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 method.",

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AU - Chen, Shanqin

AU - Weinan, E.

AU - Shu, Chi Wang

PY - 2005

Y1 - 2005

N2 - In this paper we develop a discontinuous Galerkin (DG) method, within the framework of the heterogeneous multiscale method (HMM), for solving hyperbolic and parabolic multiscale problems. Hyperbolic scalar equations and systems, as well as parabolic scalar problems, are considered. 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 method.

AB - In this paper we develop a discontinuous Galerkin (DG) method, within the framework of the heterogeneous multiscale method (HMM), for solving hyperbolic and parabolic multiscale problems. Hyperbolic scalar equations and systems, as well as parabolic scalar problems, are considered. 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 method.

KW - Discontinuous Galerkin method

KW - Heterogeneous multiscale method

KW - Homogenization

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ER -

The heterogeneous multiscale method based on the discontinuous Galerkin method for hyperbolic and parabolic problems

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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