Residual-based a posteriori error estimate for hypersingular equation on surfaces

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.