Data Oscillation and Convergence of Adaptive FEM

Data oscillation is intrinsic information missed by the averaging process associated with nite element methods (FEM) regardless of quadra-ture. Ensuring a reduction rate of data oscillation, together with an error reduction based on a posteriori error estimators, we construct a simple and eecient adaptive FEM for elliptic PDE with linear rate of convergence without any preliminary mesh adaptation nor explicit knowledge of constants. Any prescribed error tolerance is thus achieved in a nite number of steps. A number of numerical experiments in 2d and 3d yield quasi-optimal meshes along with a competitive performance.