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

Shanqin Chen, Weinan E, Chi Wang Shu

Research output: Chapter in Book/Report/Conference proceedingConference 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 languageEnglish (US)
Title of host publication3rd M.I.T. Conference on Computational Fluid and Solid Mechanics
Pages1072-1075
Number of pages4
StatePublished - Dec 1 2005
Event3rd M.I.T. Conference on Computational Fluid and Solid Mechanics - Boston, MA, United States
Duration: Jun 14 2005Jun 17 2005

Publication series

Name3rd M.I.T. Conference on Computational Fluid and Solid Mechanics

Other

Other3rd M.I.T. Conference on Computational Fluid and Solid Mechanics
CountryUnited States
CityBoston, MA
Period6/14/056/17/05

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

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