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A Posteriori Error Estimation for Adaptive Discontinuous Galerkin Approximations of Hyperbolic Systems

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Discontinuous Galerkin Methods

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 11))

Abstract

This article considers a posteriori error estimation of specified functionals for first-order systems of conservation laws discretized using the discontinuous Galerkin (DG) finite element method. Using duality techniques, we derive exact error representation formulas for both linear and nonlinear functionals given an associated bilinear or nonlinear variational form. Weighted residual approximations of the exact error representation formula are then proposed and numerically evaluated for Ringleb flow, an exact solution of the 2-D Euler equations.

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Author information

Authors and Affiliations

  1. Mechanics and Computation, Stanford University, Stanford, CA, 94305, USA

    Mats G. Larson

  2. NAS Division, NASA Ames Research Center, Moffett Field, CA, 94035, USA

    Timothy J. Barth

Authors
  1. Mats G. Larson
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  2. Timothy J. Barth
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Editor information

Editors and Affiliations

  1. School of Mathematics, University of Minnesota, 206 Church Street S.E., Minneapolis, MN, 55455, USA

    Bernardo Cockburn

  2. Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA

    George E. Karniadakis  & Chi-Wang Shu  & 

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© 2000 Springer-Verlag Berlin Heidelberg

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Larson, M.G., Barth, T.J. (2000). A Posteriori Error Estimation for Adaptive Discontinuous Galerkin Approximations of Hyperbolic Systems. In: Cockburn, B., Karniadakis, G.E., Shu, CW. (eds) Discontinuous Galerkin Methods. Lecture Notes in Computational Science and Engineering, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59721-3_34

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  • DOI: https://doi.org/10.1007/978-3-642-59721-3_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64098-8

  • Online ISBN: 978-3-642-59721-3

  • eBook Packages: Springer Book Archive

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