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hp–Adaptive Two-Grid Discontinuous Galerkin Finite Element Methods for Quasi-Newtonian Fluid Flows

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Numerical Mathematics and Advanced Applications 2011

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Abstract

We develop the a posteriori error analysis, with respect to a mesh–dependent energy norm, of two-grid hp–version discontinuous Galerkin finite element methods for quasi-Newtonian flows. The performance of the proposed estimators within an hp–adaptive refinement procedure is studied through a numerical experiment.

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References

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Acknowledgements

PH acknowledges the financial support of the EPSRC under the grant EP/H005498. TW acknowledges the financial support of the SNF No. 200021}126594.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK

    S. Congreve & P. Houston

  2. Mathematisches Institut, Universität Bern, Sidlerstrasse 5, CH-3012, Bern, Switzerland

    T. P. Wihler

Authors
  1. S. Congreve
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  2. P. Houston
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  3. T. P. Wihler
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Corresponding author

Correspondence to S. Congreve .

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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Congreve, S., Houston, P., Wihler, T.P. (2013). hp–Adaptive Two-Grid Discontinuous Galerkin Finite Element Methods for Quasi-Newtonian Fluid Flows. 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_37

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