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A posteriori error bounds in boundary layer theory

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Abstract

The subject of this paper is the two-dimensional steady laminar boundary layer of an incompressible medium at a wall. For a given approximate solution of the Prandtl equation, error bounds are computed with the aid of parabolic inequalities. Also, bounds for the wall shear stress, for the displacement thickness, for the momentum loss thickness, and for the energy loss thickness are given. The bounds converge toward zero if the residual error and the initial error of the approximation both vanish.

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Authors and Affiliations

  1. Institut für Praktische Mathematik Universität Karlsruhe, 75, Karlsruhe

    Karl L. Nickel

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  1. Karl L. Nickel
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Communicated by J.Serrin

This research was sponsored by the United States Army under Contract No.: DA-31-124-ARO-D-462. This paper was written while the author was a member of the Mathematics Research Center, University of Wisconsin, Madison, Wisconsin, USA. It has appeared previously as MRC Technical Summary Report #1143, April 16, 1971. Some parts of it were presented at the Second International Conference on Numerical Methods in Fluid Dynamics at the University of California, Berkeley, California, 1970, and are published in the Proceedings of this symposium [6].

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Nickel, K.L. A posteriori error bounds in boundary layer theory. Arch. Rational Mech. Anal. 53, 14–39 (1973). https://doi.org/10.1007/BF00735698

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  • DOI: https://doi.org/10.1007/BF00735698

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