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Reconstruction-Based a Posteriori Error Estimators for the Transport Equation

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Book cover Numerical Mathematics and Advanced Applications 2011

Abstract

We present a unified approach to build error estimators based on H(div)-reconstructed fluxes on the primal mesh, inspired by the hypercircle method. Here, the transport equation is considered and discretized by discontinuous Galerkin, nonconforming and conforming finite elements. We describe the local computation of fluxes on patches, obtain upper error bounds and show some numerical tests.

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References

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Author information

Authors and Affiliations

  1. EPI Concha & LMA CNRS UMR 5142 – INRIA Bordeaux Sud-Ouest & Université de Pau,IPRA, 1155, 64013, Pau, France

    R. Becker, D. Capatina & R. Luce

Authors
  1. R. Becker
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  2. D. Capatina
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  3. R. Luce
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Corresponding author

Correspondence to R. Becker .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, University of Leicester, Leicester, LE!1 7RH, United Kingdom

    Andrea Cangiani

  2. , Department of Mathematics, University of Leicester, Leicester, LE1 7RL, United Kingdom

    Ruslan L. Davidchack

  3. , Department of Mathematics, University of Leicester, Leicester, LE1 7RH, United Kingdom

    Emmanuil Georgoulis

  4. , Department of Mathematics, University of Leicester, Leicester, LE1 7RH, United Kingdom

    Alexander N. Gorban

  5. , Department of Mathematics, University of Leicester, Leicester, LE1 7RH, United Kingdom

    Jeremy Levesley

  6. , School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom

    Michael V. Tretyakov

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© 2013 Springer-Verlag Berlin Heidelberg

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Becker, R., Capatina, D., Luce, R. (2013). Reconstruction-Based a Posteriori Error Estimators for the Transport Equation. In: Cangiani, A., Davidchack, R., Georgoulis, E., Gorban, A., Levesley, J., Tretyakov, M. (eds) Numerical Mathematics and Advanced Applications 2011. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33134-3_2

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