Data oscillation and convergence of adaptive FEM

Abstract. 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 oscil-lation, 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 conver-gence 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. Key words. a posteriori error estimators, data oscillation, adaptive mesh refinement, conver-gence, performance, quasi-optimal meshe