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An experimental survey of a posteriori Courant finite element error control for the Poisson equation

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Abstract

This comparison of some a posteriori error estimators aims at empirical evidence for a ranking of their performance for a Poisson model problem with conforming lowest order finite element discretizations. Modified residual-based error estimates compete with averaging techniques and two estimators based on local problem solving. Multiplicative constants are involved to achieve guaranteed upper and lower energy error bounds up to higher order terms. The optimal strategy combines various estimators.

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Authors and Affiliations

  1. Institute for Applied Mathematics and Numerical Analysis, Vienna University of Technology, Wiedner Hauptstraße 8-10/115, A-1040, Vienna, Austria

    Carsten Carstensen

  2. Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Str. 4, D-24098, Kiel, Germany

    Sören Bartels & Roland Klose

Authors
  1. Carsten Carstensen
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  2. Sören Bartels
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  3. Roland Klose
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Correspondence to Roland Klose.

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Carstensen, C., Bartels, S. & Klose, R. An experimental survey of a posteriori Courant finite element error control for the Poisson equation. Advances in Computational Mathematics 15, 79–106 (2001). https://doi.org/10.1023/A:1014269318616

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