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Equadiff 6 pp 327–332Cite as

Free boundary problems for stokes' flows and finite element methods

Lectures Presented In Sections

Part of the Lecture Notes in Mathematics book series (LNM,volume 1192)

Abstract

In two dimensions a Stokes' flow is considered symmetric to the abscissa η=0 and periodic with respect to ξ. On the free boundary |η|=S(ξ) the conditions are: (i) the free boundary is a streamline, (ii) the tangential force vanishes, (iii) the normal force is proportional to the mean curvature of the boundary. By straightening the boundary, i. e. by introducing the variables x=ξ, y=η/S(ξ), the problem is reduced to one in a fixed domain. The underlying differential equations are now highly nonlinear: They consist in an elliptic system coupled with an ordinary differential equation for S. The analytic properties of the solution as well as the convergence of the proposed finite element approximation are discussed.

Keywords

  • Free Boundary
  • Tangential Force
  • Elliptic System
  • Free Boundary Problem
  • Approximation Space

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References

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© 1986 Equadiff 6 and Springer-Verlag

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Nitsche, J.A. (1986). Free boundary problems for stokes' flows and finite element methods. In: Vosmanský, J., Zlámal, M. (eds) Equadiff 6. Lecture Notes in Mathematics, vol 1192. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076089

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  • DOI: https://doi.org/10.1007/BFb0076089

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16469-2

  • Online ISBN: 978-3-540-39807-3

  • eBook Packages: Springer Book Archive