  In the present work, we consider weakly-singular integral equations arising
from linear second-order strongly-elliptic PDE systems with constant
coefficients, including, e.g., linear elasticity. We introduce a general
framework for optimal convergence of adaptive Galerkin BEM. We identify certain
abstract properties for the underlying meshes, the corresponding
mesh-refinement strategy, and the ansatz spaces that guarantee convergence at
optimal algebraic rate of an adaptive algorithm driven by the weighted-residual
error. These properties are satisfied, e.g., for discontinuous piecewise
polynomials on simplicial meshes as well as certain ansatz spaces used for
isogeometric analysis. Technical contributions include local inverse estimates
for the (non-local) boundary integral operators associated to the PDE system.
