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A posteriori error estimates for nonconforming finite element methods

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Summary.

Computable a posteriori error bounds for a large class of nonconforming finite element methods are provided for a model Poisson-problem in two and three space dimensions. Besides a refined residual-based a posteriori error estimate, an averaging estimator is established and an \(L^2\)-estimate is included. The a posteriori error estimates are reliable and efficient; the proof of reliability relies on a Helmholtz decomposition.

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Authors and Affiliations

  1. Institute for Applied Mathematics and Numerical Analysis, Vienna University of Technology, Wiedner Hauptstraße 8–10, A-1040 Vienna, Austria; e-mail: Carsten.Carstensen@tuwien.ac.at , , , , , , AT

    Carsten Carstensen

  2. Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Str. 4, 24098 Kiel, Germany; e-mail: sba@numerik.uni-kiel.de , , , , , , DE

    Sören Bartels & Stefan Jansche

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  1. Carsten Carstensen
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  2. Sören Bartels
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  3. Stefan Jansche
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Received March 4, 1997 / Revised version received September 4, 2001 / Published online December 18, 2001

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Carstensen, C., Bartels, S. & Jansche, S. A posteriori error estimates for nonconforming finite element methods. Numer. Math. 92, 233–256 (2002). https://doi.org/10.1007/s002110100378

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  • DOI: https://doi.org/10.1007/s002110100378

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