Numerische Mathematik

, Volume 74, Issue 4, pp 419–451 | Cite as

Boundary element collocation methods using splines with multiple knots

  • W. McLean
  • S.B. Prößdorf

Summary.

We extend the theory of boundary element collocation methods by allowing reduced inter-element smoothness (or in other words, by allowing trial functions that are splines with multiple knots). Our convergence analysis is based on a recurrence relation for the Fourier coefficients of the numerical solution, and so is restricted to uniform grids on smooth, closed curves. Superconvergence is possible with special choices of the collocation points. Numerical experiments with a model problem confirm the convergence rates predicted by our theory.

Mathematics Subject Classification (1991): 65N38, 41A15, 65N12, 35S99, 42A16 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • W. McLean
    • 1
  • S.B. Prößdorf
    • 2
  1. 1.School of Mathematics, The University of New South Wales, Sydney 2052, Australia; e-mail: W.McLean@unsw.edu.auAU
  2. 2.Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstraße 39, D-10117 Berlin, GermanyDE

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