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On the convergence of adaptive feedback loops

  • Special Issue CS Symposium 2016
  • Published:
Computing and Visualization in Science

Abstract

We present a technique for proving convergence of h and hp adaptive finite element methods through comparison with certain reference refinement schemes based on interpolation error. We then construct a testing environment where properties of different adaptive approaches can be evaluated and improved.

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Notes

  1. Finding the maximum will introduce a logarithm into the complexity (e.g., we keep all the elements in a heap based on their errors), but this is not important in this context.

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Authors and Affiliations

  1. Department of Mathematics, University of California, San Diego, La Jolla, CA, 92093-0112, USA

    Randolph E. Bank

  2. Institut für Mathematik, Technische Universität Berlin, 10623, Berlin, Germany

    Harry Yserentant

Authors
  1. Randolph E. Bank
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  2. Harry Yserentant
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Correspondence to Randolph E. Bank.

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Communicated by Volker Schulz.

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Randolph E. Bank: The work of this author was supported by the National Science Foundation under Contract DMS-1318480, and the Alexander von Humboldt Foundation through a Humboldt Research Award.

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Bank, R.E., Yserentant, H. On the convergence of adaptive feedback loops. Comput. Visual Sci. 20, 59–70 (2019). https://doi.org/10.1007/s00791-019-00310-4

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  • DOI: https://doi.org/10.1007/s00791-019-00310-4

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