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C. Carstensen, M. Maischak, E. Stephan, D. Praetorius:
"Residual-based a posteriori error estimate for hypersingular equation on surfaces";
Numerische Mathematik, 97 (2004), 3; 397 - 426.

The hypersingular integral equation of the first kind equivalently
describes screen and Neumann problems on an open surface piece. The
paper establishes a computable upper error bound for its Galerkin
approximation and so motivates adaptive mesh refining algorithms.
Numerical experiments for triangular elements on a screen provide
empirical evidence of the superiority of adapted over uniform
mesh-refining. The numerical realisation requires the evaluation of
the hypersingular integral operator at a source point; this and\
other details on the algorithm are included.

http://www.anum.tuwien.ac.at/~dirk/download/published/cmps_numermath97.pdf