Numerische Mathematik

, Volume 28, Issue 4, pp 431–443

Error estimates for the finite element solution of variational inequalities

Part I. Primal theory
  • Franco Brezzi
  • William W. Hager
  • P. A. Raviart

DOI: 10.1007/BF01404345

Cite this article as:
Brezzi, F., Hager, W.W. & Raviart, P.A. Numer. Math. (1977) 28: 431. doi:10.1007/BF01404345


We analyze the convergence of finite element approximations of some variational inequalities namely the “obstacle problem” and the “unilateral problem”. OptimalO(h) andO(h3/2−∈) error bounds for the obstacle problem (for linear and quadratic elements) and anO(h) error bound for the unilateral problem (with linear elements) are proved.

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • Franco Brezzi
    • 1
  • William W. Hager
    • 2
  • P. A. Raviart
    • 3
  1. 1.Politecnico di Torino and Laboratorio di Analisi Numerica del C.N.R.PaviaItaly
  2. 2.Department of MathematicsCarnegie-Mellon UniversityPittsburghUSA
  3. 3.Analyse NumériqueUniversité Pierre et Marie CurieParis Cedex 05France