Numerische Mathematik

, Volume 56, Issue 8, pp 735–762

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

  • Uday Banerjee
  • John E. Osborn

DOI: 10.1007/BF01405286

Cite this article as:
Banerjee, U. & Osborn, J.E. Numer. Math. (1989) 56: 735. doi:10.1007/BF01405286


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): 65D3065N1565N2565N30CR: G 1.8

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