Numerische Mathematik

, Volume 56, Issue 8, pp 735–762 | Cite as

Estimation of the effect of numerical integration in finite element eigenvalue approximation

  • Uday Banerjee
  • John E. Osborn
Article

Summary

Finite element approximations of the eigenpairs of differential operators are computed as eigenpairs of matrices whose elements involve integrals which must be evaluated by numerical integration. The effect of this numerical integration on the eigenvalue and eigenfunction error is estimated. Specifically, for 2nd order selfadjoint eigenvalue problems we show that finite element approximations with quadrature satisfy the well-known estimates for approximations without quadrature, provided the quadrature rules have appropriate degrees of precision.

Subject Classifications

AMS(MOS): 65D30 65N15 65N25 65N30 CR: G 1.8 

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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Uday Banerjee
    • 1
  • John E. Osborn
    • 2
  1. 1.Department of MathematicsSyracuse UniversitySyracuseUSA
  2. 2.Department of MathematicsUniversity of MarylandCollege ParkUSA

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