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Numerical Mathematics and Advanced Applications 2009 pp 397–405Cite as

On Hierarchical Error Estimators for Time-Discretized Phase Field Models

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Abstract

We suggest hierarchical a posteriori error estimators for time-discretized Allen–Cahn and Cahn–Hilliard equations with logarithmic potential and investigate their robustness numerically. We observe that the associated effectivity ratios seem to saturate for decreasing mesh size and are almost independent of the temperature.

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Acknowledgement

This work was supported by the DFG Research Center Matheon

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Authors and Affiliations

  1. Freie Universität Berlin, Berlin, Germany

    Carsten Gräser, Ralf Kornhuber & Uli Sack

Authors
  1. Carsten Gräser
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  2. Ralf Kornhuber
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  3. Uli Sack
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Corresponding author

Correspondence to Carsten Gräser .

Editor information

Editors and Affiliations

  1. Dept. of Information Technology, Uppsala University, Uppsala, 751 05, Sweden

    Gunilla Kreiss

  2. Dept. of Information Technology, Uppsala University, Uppsala, 751 05, Sweden

    Per Lötstedt

  3. Dept. of Information Technology, Uppsala University, Uppsala, 751 05, Sweden

    Axel Målqvist

  4. Dept. of Information Technology, Uppsala University, Uppsala, 751 05, Sweden

    Maya Neytcheva

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Gräser, C., Kornhuber, R., Sack, U. (2010). On Hierarchical Error Estimators for Time-Discretized Phase Field Models. In: Kreiss, G., Lötstedt, P., Målqvist, A., Neytcheva, M. (eds) Numerical Mathematics and Advanced Applications 2009. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11795-4_42

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