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Numerical Algorithms

, Volume 39, Issue 1–3, pp 143–154 | Cite as

Wavelets and adaptive grids for the discontinuous Galerkin method

  • Jorge L. Díaz Calle
  • Philippe R. B. Devloo
  • Sônia M. Gomes
Article

Abstract

In this paper, space adaptivity is introduced to control the error in the numerical solution of hyperbolic systems of conservation laws. The reference numerical scheme is a new version of the discontinuous Galerkin method, which uses an implicit diffusive term in the direction of the streamlines, for stability purposes. The decision whether to refine or to unrefine the grid in a certain location is taken according to the magnitude of wavelet coefficients, which are indicators of local smoothness of the numerical solution. Numerical solutions of the nonlinear Euler equations illustrate the efficiency of the method.

Keywords

conservation laws discontinuous Galerkin implicit time integration upwind artificial diffusion adaptivity wavelets 

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Copyright information

© Springer 2005

Authors and Affiliations

  • Jorge L. Díaz Calle
    • 1
  • Philippe R. B. Devloo
    • 2
  • Sônia M. Gomes
    • 3
  1. 1.Commodity SystemsSão Paulo SPBrasil
  2. 2.FECUniversidade Estadual de CampinasCampinas SPBrasil
  3. 3.IMECCUniversidade Estadual de CampinasCampinas SPBrasil

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