Some Gradient Superconvergence Results in the Finite Element Method

  • J. R. Whiteman
  • G. Goodsell
Chapter
Part of the Lecture Notes in Mathematics book series (LNM)

Abstract

This paper is concerned with the phenomenon of gradient superconvergence of finite element approximations to the solutions of two-dimensional second order elliptic boundary value problems. The original concept of gradient superconvergence is that there exist certain points in each element at which the gradient of the finite element approximation has a higher rate of convergence to the gradient of the true solution in a discrete analogue of a Lebesgue norm than that found globally in the Lebesgue norm itself.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • J. R. Whiteman
    • 1
  • G. Goodsell
    • 1
  1. 1.Institute of Computational Mathematics, Department of Mathematics and StatisticsBrunel UniversityUxbridgeEngland

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