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Numerische Mathematik

, Volume 128, Issue 4, pp 615–634 | Cite as

An adaptive finite element method with asymptotic saturation for eigenvalue problems

  • C. Carstensen
  • J. Gedicke
  • V. Mehrmann
  • A. Międlar
Article

Abstract

This paper discusses adaptive finite element methods for the solution of elliptic eigenvalue problems associated with partial differential operators. An adaptive method based on nodal-patch refinement leads to an asymptotic error reduction property for the computed sequence of simple eigenvalues and eigenfunctions. This justifies the use of the proven saturation property for a class of reliable and efficient hierarchical a posteriori error estimators. Numerical experiments confirm that the saturation property is present even for very coarse meshes for many examples; in other cases the smallness assumption on the initial mesh may be severe.

Mathematics Subject Classification (1991)

65N15 65N25 65N30 

Notes

Acknowledgments

The authors would like to thank the anonymous referees for their valuable comments and suggestions.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • C. Carstensen
    • 1
    • 2
  • J. Gedicke
    • 3
  • V. Mehrmann
    • 4
  • A. Międlar
    • 4
  1. 1.Humboldt-Universität zu BerlinBerlinGermany
  2. 2.Department of Computational Science and EngineeringYonsei UniversitySeoulKorea
  3. 3.Department of Mathematics and Center for Computation and TechnologyLouisiana State UniversityBaton RougeUSA
  4. 4.Institut für Mathematik, MA 4-5 TU BerlinBerlinGermany

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