Error bounds in boundary layer theory

  • Karl L. E. Nickel
Session III Boundary Layers
Part of the Lecture Notes in Physics book series (LNP, volume 8)


The two dimensional steady laminar boundary layer of an incompressible medium is treated. The paper consists of two sections. In the first section a priori error bounds for the unknown solution of the Prandtl equation are given. Included are bounds for the wall shear stress, for the displacement thickness and for the momentum loss thickness; also an a priori upstream bound for the separation point is evaluated. In the second section for a given approximate solution error bounds are computed with the aid of the theory of parabolic inequalities. The bounds converge toward zero if the residual error vanishes.


Wall Shear Stress Residual Error Admissible Function Boundary Layer Theory Displacement Thickness 
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  1. [1]
    Nickel, K.: Einige Eigenschaften von Loesungen der Prandtlschen Grenzschichtdifferentialgleichungen. Archive Rat. Mech. Analysis 2, 1–31 (1958).Google Scholar
  2. [2]
    Nickel, K.: Ein Eindeutigkeitssatz fuer instationaere Grenzschichten I und II. Math. Zeitschr. 74, 209–220 (1960) and 83, 1–7 (1964).Google Scholar
  3. [3]
    Nickel, K.: Parabolic equations with application to boundary layer theory. Partial Differential Equations and Continuum Mechanics, Madison, Wisconsin 1961, 319–330.Google Scholar
  4. [4]
    Nickel, K.: Eine einfache Abschaetzung fuer Grenzschichten. Ing.-Archiv 31, 85–100 (1962).Google Scholar

Copyright information

© Springer-Verlag 1971

Authors and Affiliations

  • Karl L. E. Nickel
    • 1
    • 2
  1. 1.Universitaet KarlsruheGermany
  2. 2.Mathematics Research CenterUniversity of WisconsinMadisonUSA

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