Numerische Mathematik

, Volume 91, Issue 1, pp 1–12

Small data oscillation implies the saturation assumption

  • Willy Dörfler
  • Ricardo H. Nochetto
Original article


The saturation assumption asserts that the best approximation error in \(H^1_0\) with piecewise quadratic finite elements is strictly smaller than that of piecewise linear finite elements. We establish a link between this assumption and the oscillation of \(f=-\Delta u\), and prove that small oscillation relative to the best error with piecewise linears implies the saturation assumption. We also show that this condition is necessary, and asymptotically valid provided \(f\in L^2\).

Mathematics Subject Classification (1991): 65N15, 65N30, 65N50 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Willy Dörfler
    • 1
  • Ricardo H. Nochetto
    • 2
  1. 1.FB Mathematik, Universität Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany; e-mail: DE
  2. 2.Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA; e-mail: US

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