Advertisement

Quadrature error of the load vector in the finite element method

  • Chang -Geun Kim
Article
  • 50 Downloads

Abstract

We analyze the error in thep version of the of the finite element method when the effect of the quadrature error is taken in the load vector. We briefly study some results on theH 1 norm error and present some new results for the error in theL 2 norm. We investigate the quadrature error due to the numerical integration of the right hand side We present theoretical and computational examples showing the sharpness of our results.

AMS Mathematics Subject Classification

65N30 68U20 68D99 

Key word and phrases

quadrature error H1 norm error L2 norm error finite element method p-version 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    I. Babuška, B. Guo, and M. Suri.Implementation of non-homogeneous Dirichlet boundary conditions in the p-version of the finite element method. Impact of Computing in Science and Engineering1 (1989), 36–63.MATHCrossRefGoogle Scholar
  2. 2.
    I. Babuška and M. Suri.The optimal convergence rate of the p-version of the finite element method. SIAM J. Numer. Anal.24, (1987), 750–776.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    U. Banerjee and M. Suri.The effect of numerical quadrature in the p version of the finite element method. Math. Comp.59 (1992), 1–20.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    C. Bernardi and Y. Maday.Approximations spectrales de problemes aux limites elliptiques. Technical report, 1991.Google Scholar
  5. 5.
    P. G. Ciarlet.The Finite Element Method for Elliptic Problems. North Holland, Amsterdam, 1978.MATHCrossRefGoogle Scholar
  6. 6.
    P. J. Davis and P. Rabinowitz.Methods of Numerical Integration. Academic Press, New York, 1975.MATHGoogle Scholar
  7. 7.
    M. R. Dorr.The approximation theory for the p-version of the finite element method. SIAM J. Numer. Anal.21 (1984), 1180–1207.MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    S. Jensen and M. Suri,On the L 2 error for the p version of the finite element method over polygonal domains. Comp. Meth. Appl. Mech. Eng.97 (1992), 233–243.MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    M. Suri.The p-version of the finite element method for elliptic equations of order 2ℓ. RAIRO Math. Mod. Numer. Anal.24 (1990), 107–146MathSciNetGoogle Scholar

Copyright information

© Korean Society for Computational and Applied Mathematics 1998

Authors and Affiliations

  1. 1.Department of Mathematics Research Institute of Basic ScienceKwangwoon UniversitySeoulKorea

Personalised recommendations