Numerische Mathematik

, Volume 118, Issue 3, pp 401–427 | Cite as

An oscillation-free adaptive FEM for symmetric eigenvalue problems

  • Carsten CarstensenEmail author
  • Joscha Gedicke


A refined a posteriori error analysis for symmetric eigenvalue problems and the convergence of the first-order adaptive finite element method (AFEM) is presented. The H 1 stability of the L 2 projection provides reliability and efficiency of the edge-contribution of standard residual-based error estimators for P 1 finite element methods. In fact, the volume contributions and even oscillations can be omitted for Courant finite element methods. This allows for a refined averaging scheme and so improves (Mao et al. in Adv Comput Math 25(1–3):135–160, 2006). The proposed AFEM monitors the edge-contributions in a bulk criterion and so enables a contraction property up to higher-order terms and global convergence. Numerical experiments exploit the remaining L 2 error contributions and confirm our theoretical findings. The averaging schemes show a high accuracy and the AFEM leads to optimal empirical convergence rates.

Mathematics Subject Classification (2000)

65N12 65N25 65N30 65N50 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Institut für MathematikHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Department of Computational Science and EngineeringYonsei UniversitySeoulKorea

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