h-adaptive least-squares finite element methods for the 2D Stokes equations of any order with optimal convergence rates

The adaptive least-squares finite element method (LS-FEM) for the Stokes equations has recently been based on alternative error estimators in Bringmann and Carstensen (2016) for the lowest-order case. Since the first-order div LS-FEM measures the flux errors in H(div), the data resolution error measures the L2 norm of the right-hand side f minus the piecewise polynomial approximation Πkf without a mesh-size factor. This enforces separate marking with an overall abstract theory (Carstensen and Rabus, 2016). This paper contributes (a) a discussion of the scaling of the LS-FEM, (b) optimal rates of the adaptive h-version of any order k, and (c) comparing numerical results in 2D with all details on inhomogeneous Dirichlet data covered by the analysis.