  We consider h-adaptive algorithms in the context of the finite element method
(FEM) and the boundary element method (BEM). Under quite general assumptions on
the building blocks SOLVE, ESTIMATE, MARK, and REFINE of such algorithms, we
prove plain convergence in the sense that the adaptive algorithm drives the
underlying a posteriori error estimator to zero. Unlike available results in
the literature, our analysis avoids the use of any reliability and efficiency
estimate, but only relies on structural properties of the estimator, namely
stability on non-refined elements and reduction on refined elements. In
particular, the new framework thus covers also problems involving non-local
operators like the fractional Laplacian or boundary integral equations, where
(discrete) efficiency is (currently) not available.
