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Equadiff 6 pp 327-332 | Cite as

Free boundary problems for stokes' flows and finite element methods

  • J. A. Nitsche
Lectures Presented In Sections Section C Numerical Methods
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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Equadiff 6 and Springer-Verlag 1986

Authors and Affiliations

  • J. A. Nitsche
    • 1
  1. 1.Institut für angewandte MathematikAlbert-Ludwigs-UniversitätFreiburg im BreisgauGermany

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