Convergence of adaptive finite element methods with error-dominated oscillation

Abstract

Recently, we devised an approach to a posteriori error analysis, which clarifies the role of oscillation and where oscillation is bounded in terms of the current approximation error. Basing upon this approach, we derive plain convergence of adaptive linear finite elements approximating the Poisson problem. The result covers arbritray H^-1-data and characterizes convergent marking strategies.