Numerische Mathematik

, Volume 45, Issue 1, pp 105–116

Superconvergence phenomenon in the finite element method arising from averaging gradients

Authors

  • Michal Křížek
    • Mathematical InstituteCzechoslovak Academy of Sciences
  • Pekka Neittaanmäki
    • Department of MathematicsUniversity of Jyväskylä
A Short Note on Romberg Integration

DOI: 10.1007/BF01379664

Cite this article as:
Křížek, M. & Neittaanmäki, P. Numer. Math. (1984) 45: 105. doi:10.1007/BF01379664

Summary

We study a superconvergence phenomenon which can be obtained when solving a 2nd order elliptic problem by the usual linear elements. The averaged gradient is a piecewise linear continuous vector field, the value of which at any nodal point is an average of gradients of linear elements on triangles incident with this nodal point. The convergence rate of the averaged gradient to an exact gradient in theL 2-norm can locally be higher even by one than that of the original piecewise constant discrete gradient.

Subject Classifications

AMS(MOS) 65 N 30 CR: 5.17

Copyright information

© Springer-Verlag 1984