  We show that adaptive least-squares finite element methods driven by the
canonical least-squares functional converge under weak conditions on PDE
operator, mesh-refinement, and marking strategy. Contrary to prior works, our
plain convergence does neither rely on sufficiently fine initial meshes nor on
severe restrictions on marking parameters. Finally, we prove that convergence
is still valid if a contractive iterative solver is used to obtain the
approximate solutions (e.g., the preconditioned conjugate gradient method with
optimal preconditioner). The results apply within a fairly abstract framework
which covers a variety of model problems.

Numerical Analysis;Numerical Analysis