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A Numerical Study of Averaging Error Indicators in p-FEM

  • Philipp Dörsek
  • J. Markus Melenk
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 95)

Abstract

We consider the averaging error indicator in the context of the p-FEM. We explain how a proof of reliability and efficiency might look, and why the error indicator will behave differently than for low order methods. Using two model problems, one with nonsmooth, the other one with smooth solution, we identify appropriate spaces for the averaged fluxes in order to obtain reasonable reliability and efficiency bounds on the averaging error indicator for p-FEM. In particular, averaging over two neighbouring elements using global polynomials of the same polynomial degree as the finite element solution leads to reliability and efficiency up to a factor of order O(p).

Notes

Acknowledgements

The first author gratefully acknowledges support by the ETH Foundation.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.ETH ZürichZürichSwitzerland
  2. 2.Vienna University of TechnologyViennaAustria

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