This article is dedicated to the adaptive wavelet boundary element method. It computes an approximation to the unknown solution of the boundary integral equation under consideration with a rate N~(-s)_(dof), whenever the solution can be approximated with this rate in the setting determined by the underlying wavelet basis. The computational cost scale linearly in the number N_(dof) of degrees of freedom. Goal-oriented error estimation for evaluating linear output functionals of the solution is also considered. An algorithm is proposed that approximately evaluates a linear output functional with a rate N~(-(s+1))_(dof) , whenever the primal solution can be approximated with a rate N~(-s)_(dof) and the dual solution can be approximated with a rate N~(-t)_(dof) while the cost still scale linearly in N_(dof). Numerical results for an acoustic scattering problem and for the point evaluation of the potential in case of the Laplace equation are reported to validate and quantify the approach.
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