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Discontinuous Galerkin Methods pp 349–354Cite as

A Posteriori Error Estimate in the Case of Insufficient Regularity of the Discrete Space

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

Abstract

We derive a posteriori error estimates for the nonconforming rotated bilinear element. The estimates are residual based and make use of weight factors obtained by a duality argument. Galerkin orthogonality requires the introduction of additional local trial functions. We show that their influence is of higher order and that they can be neglected. The validity of the estimate is demonstrated by computations for the Laplacian and for Stokes’ equations.

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References

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Author information

Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Heidelberg, INF 294, 69120, Heidelberg, Germany

    Guido Kanschat

  2. Fachbereich Mathematik, Lehrstuhl X, Universität Dortmund, Vogelpothsweg 87, 44221, Dortmund, Germany

    Franz-Theo Suttmeier

Authors
  1. Guido Kanschat
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  2. Franz-Theo Suttmeier
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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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Kanschat, G., Suttmeier, FT. (2000). A Posteriori Error Estimate in the Case of Insufficient Regularity of the Discrete Space. 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_32

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  • DOI: https://doi.org/10.1007/978-3-642-59721-3_32

  • 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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