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Max-norm Estimates

  • Susanne C. Brenner
  • L. Ridgway Scott
Part of the Texts in Applied Mathematics book series (TAM, volume 15)

Abstract

The finite element approximation is essentially defined by a mean-square projection of the gradient. Thus, it is natural that error estimates for the gradient of the error directly follow in the L 2 norm. It is interesting to ask whether such a gradient-projection would also be of optimal order in some other norm, for example L . We prove here that this is the case. Although of interest in their own right, such estimates are also crucial in establishing the viability of approximations of nonlinear problems (Douglas & Dupont 1975) as we indicate in Sect. 8.7. Throughout this chapter, we assume that the domain Ω ⊂ ℝ d is bounded and polyhedral.

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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Susanne C. Brenner
    • 1
  • L. Ridgway Scott
    • 2
  1. 1.Department of MathematicsUniversity of South CarolinaColumbiaUSA
  2. 2.University of ChicagoChicagoUSA

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