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On residual-based a posteriori error estimation in hp-FEM

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Abstract

A family ηα, α∈[0,1], of residual-based error indicators for the hp-version of the finite element method is presented and analyzed. Upper and lower bounds for the error indicators ηα are established. To do so, the well-known Clément/Scott–Zhang interpolation operator is generalized to the hp-context and new polynomial inverse estimates are presented. An hp-adaptive strategy is proposed. Numerical examples illustrate the performance of the error indicators and the adaptive strategy.

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Authors and Affiliations

  1. MPI für Mathematik in den Naturwissenschaften, Inselstr. 22-26, D-04103, Leipzig, Germany

    J.M. Melenk

  2. Math. Inst. A, Universität Stuttgart, Pfaffenwaldring 57, D-70569, Stuttgart, Germany

    B.I. Wohlmuth

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  1. J.M. Melenk
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  2. B.I. Wohlmuth
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Melenk, J., Wohlmuth, B. On residual-based a posteriori error estimation in hp-FEM. Advances in Computational Mathematics 15, 311–331 (2001). https://doi.org/10.1023/A:1014268310921

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