  We present and analyze an a posteriori error estimator based on mesh
refinement for the solution of the hypersingular boundary integral equation
governing the Laplacian in three dimensions. The discretization under
consideration is a non-conforming domain decomposition method based on the
Nitsche technique. Assuming a saturation property, we establish
quasi-reliability and efficiency of the error estimator in comparison with the
error in a natural (non-conforming) norm. Numerical experiments with uniform
and adaptively refined meshes confirm our theoretical results.
