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

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • M. Möller

    (University of Dortmund, Institute of Applied Mathematics (LS III))

  • D. Kuzmin

    (University of Dortmund, Institute of Applied Mathematics (LS III))

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.

Suggested Citation

  • M. Möller & D. Kuzmin, 2006. "On the Use of Slope Limiters for the Design of Recovery Based Error Indicators," Springer Books, in: Alfredo Bermúdez de Castro & Dolores Gómez & Peregrina Quintela & Pilar Salgado (ed.), Numerical Mathematics and Advanced Applications, pages 233-240, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-34288-5_16
    DOI: 10.1007/978-3-540-34288-5_16
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