The p-version of the boundary element method for
hypersingular operators on piecewise plane open surfaces
Alexei Bespalov and Norbert Heuer
Numer. Math. 100 (2), 185-209, 2005.
We prove an optimal a priori error estimate for the p-version of the
boundary element method with hypersingular operators on piecewise plane open
surfaces. The solutions of problems on open surfaces typically exhibit a
singular behavior at the edges and corners of the surface which prevent an
approximation analysis in H1.
We analyze the approximation by polynomials of typical singular
functions in fractional order Sobolev spaces thus giving, as an application,
the optimal rate of convergence of the p-version of the boundary
element method.
This paper extends the results of
[C. Schwab, M. Suri, The optimal p-version approximation of
singularities on polyhedra in the boundary element method,
SIAM J. Numer. Anal., 33 (1996), pp. 729--759]
who only considered closed surfaces where the solution is in
H1.