Data oscillation and convergence of adaptive FEM

Data oscillation is intrinsic information missed by the averaging process associated with finite element methods ( FEM) regardless of quadrature. Ensuring a reduction rate of data oscillation, together with an error reduction based on a posteriori error estimators, we construct a simple and efficient adaptive FEM for elliptic partial differential equations (PDEs) with linear rate of convergence without any preliminary mesh adaptation nor explicit knowledge of constants. Any prescribed error tolerance is thus achieved in a finite number of steps. A number of numerical experiments in two and three dimensions yield quasi-optimal meshes along with a competitive performance.