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A Comparison of Discontinuous and Continuous Galerkin Methods Based on Error Estimates, Conservation, Robustness and Efficiency

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Discontinuous Galerkin Methods

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

Abstract

The Discontinuous Galerkin Method (DGM) and Continuous Galerkin Method (CGM) are investigated and compared for the advection problem and the diffusion problem. First, error estimates for Stabilized Discontinuous Galerkin Methods (SDGMs) are presented. Then, conservation laws are discussed for the DGM and CGM. An advantage ascribed to the DGM is the local flux conservation property. It is remarked that the CGM is not only globally conservative, but locally conservative too when a simple post-processing procedure is used. Next, the robustness of different DGMs is investigated numerically. Lastly, the efficiency of the DGM and CGM is compared.

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Author information

Authors and Affiliations

  1. Division of Mechanics and Computation, Stanford University, Durand Building, Stanford, California, 94305-4040, USA

    Thomas J. R. Hughes, Gerald Engel, Luca Mazzei & Mats G. Larson

Authors
  1. Thomas J. R. Hughes
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  2. Gerald Engel
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  3. Luca Mazzei
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  4. Mats G. Larson
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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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Hughes, T.J.R., Engel, G., Mazzei, L., Larson, M.G. (2000). A Comparison of Discontinuous and Continuous Galerkin Methods Based on Error Estimates, Conservation, Robustness and Efficiency. 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_9

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  • DOI: https://doi.org/10.1007/978-3-642-59721-3_9

  • 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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