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