Polynomial Approximation Theory in Sobolev Spaces

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


We will now develop the approximation theory appropriate for the finite elements developed in Chapter 3. We take a constructive approach, defining an averaged version of the Taylor polynomial familiar from calculus. The key estimates are provided by some simple lemmas from the theory of Riesz potentials, which we derive. As a corollary, we provide a proof of Sobolev’s inequality, much in the spirit given originally by Sobolev.


Sobolev Space Polynomial Approximation Reference Element Nodal Variable Interpolation Operator 


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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

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

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