Numerische Mathematik

, Volume 79, Issue 1, pp 107–140

High order convergence for collocation of second kind boundary integral equations on polygons

  • Pascal Laubin

DOI: 10.1007/s002110050333

Cite this article as:
Laubin, P. Numer. Math. (1998) 79: 107. doi:10.1007/s002110050333


We propose collocation methods with smoothest splines to solve the integral equation of the second kind on a plane polygon. They are based on the bijectivity of the double layer potential between spaces of Sobolev type with arbitrary high regularity and involving the singular functions generated by the corners. If splines of order \(2m-1\) are used, we get quasi-optimal estimates in \(H^m\)-norm and optimal order convergence for the \(H^k\)-norm if \(0\le k\le m\). Numerical experiments are presented.

Mathematics Subject Classification (1991): 65N35, 65R20, 45B05

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Pascal Laubin
    • 1
  1. 1. Institute of Mathematics, University of Liège, Grande Traverse 12, B-4000 Liège BE