An adaptive finite element method with asymptotic saturation for eigenvalue problems

C. Carstensen, J. Gedicke, V. Mehrmann, A. Międlar

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)615-634
Number of pages20
JournalNumerische Mathematik
Issue number4
StatePublished - Dec 2014
Externally publishedYes

Bibliographical note

Funding Information:
Supported by the DFG Research Center MATHEON “Mathematics for key technologies”, and the DFG graduate school BMS “Berlin Mathematical School” in Berlin.

Publisher Copyright:
© 2014, Springer-Verlag Berlin Heidelberg.


  • 65N15
  • 65N25
  • 65N30


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