We consider the solution of second order elliptic PDEs in Rdwith inhomogeneous Dirichlet data by means of an h–adaptive FEM withfixed polynomial order p ∈ N. As model example serves the Poissonequation with mixed Dirichlet–Neumann boundary conditions, where the inhomogeneousDirichlet data are discretized by use of an H1 / 2–stableprojection, for instance, the L2–projection forp = 1 or the Scott–Zhang projection for general p ≥ 1.For error estimation, we use a residual error estimator which includes the Dirichlet dataoscillations. We prove that each H1 / 2–stable projectionyields convergence of the adaptive algorithm even with quasi–optimal convergence rate.Numerical experiments with the Scott–Zhang projection conclude the work.
