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Numerical Mathematics and Advanced Applications pp 233–240Cite as

On the Use of Slope Limiters for the Design of Recovery Based Error Indicators

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Abstract

A slope limiting approach to the design of recovery based a posteriori error indicators for P 1 finite element discretizations is presented. The smoothed gradient field is recovered at edge midpoints by means of limited averaging of adjacent slope values. As an alternative, the constant gradient values may act as upper and lower bounds to be imposed on edge gradients resulting from traditional reconstruction techniques such as averaging projection or discrete patch recovery schemes. In either case, the difference between consistent and reconstructed gradient values measured in the L 2-norm provides a usable indicator for grid adaptivity.

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References

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Author information

Authors and Affiliations

  1. Institute of Applied Mathematics (LS III), University of Dortmund, Vogelpothsweg 87, D-44227, Dortmund, Germany

    M. Möller

  2. Institute of Applied Mathematics (LS III), University of Dortmund, Vogelpothsweg 87, D-44227, Dortmund, Germany

    D. Kuzmin

Authors
  1. M. Möller
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  2. D. Kuzmin
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Editors and Affiliations

  1. Departamento de Matemática Aplicada Facultade de Matemáticas, Universidade de Santiago de Compostela, 15706, Santiago de Compostela, Spain

    Alfredo Bermúdez de Castro , Dolores Gómez  & Peregrina Quintela ,  & 

  2. Departamento de Matématica Aplicada, Escola Politécnica Superior, 27002, Lugo, Spain

    Pilar Salgado

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Möller, M., Kuzmin, D. (2006). On the Use of Slope Limiters for the Design of Recovery Based Error Indicators. In: de Castro, A.B., Gómez, D., Quintela, P., Salgado, P. (eds) Numerical Mathematics and Advanced Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34288-5_16

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