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Aspects of Guaranteed Error Control in CPDEs

  • C. CarstensenEmail author
  • C. Merdon
  • J. Neumann
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 45)

Abstract

Whenever numerical algorithms are employed for a reliable computational forecast, they need to allow for an error control in the final quantity of interest. The discretization error control is of some particular importance in computational PDEs (CPDEs) where guaranteed upper error bound (GUB) are of vital relevance. After a quick overview over energy norm error control in second-order elliptic PDEs, this paper focuses on three particular aspects: first, the variational crimes from a nonconforming finite element discretization and guaranteed error bounds in the discrete norm with improved postprocessing of the GUB; second, the reliable approximation of the discretization error on curved boundaries; and finally, the reliable bounds of the error with respect to some goal functional, namely, the error in the approximation of the directional derivative at a given point.

Keywords

Guaranteed error control Equilibration error estimators Poisson model problem Conforming finite element methods Crouzeix–Raviart nonconforming finite element methods Curved boundaries Guaranteed goal-oriented error control 

Notes

Acknowledgements

This work was written while the first author enjoyed the kind hospitality of the Oxford PDE Centre.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Humboldt-Universität zu BerlinBerlinGermany
  2. 2.Department of Computational Science and EngineeringYonsei UniversitySeoulKorea
  3. 3.Weierstraß-InstitutBerlinGermany

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