There's a body of work out there dealing with the discrete convergence of adaptive finite element methods using error estimators. Most deal with proving the property$\|u-u_{k+1}\|_U \leq (1-\alpha) \|u-u_{k}\|_U, \quad  0<\alpha < 1$ by relying on Galerkin orthogonality, monotonicity of error, error estimator information, and some other tricks to bound $\| u_{k+1}-u_k\|_U \geq \alpha\|u-u_k\|_U$.  I'm curious about minimum residual (least squares) finite element methods - there's Galerkin orthogonality, minimization/monotonicity of error, and a built in error estimator (the residual in the proper norm), but I haven't found any work proving convergence of adaptive minimum residual finite element methods.  Am I overlooking some papers, or is there a roadblock to proving adaptive convergence for minimum residual FEM?
Proving convergence of adaptive finite elements - min res FEM?
finite element;error estimation;adaptive mesh refinement;least squares