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 oscillation, together with an error reduction based on a posteriori error estimators, we construct a simple and efficient 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 finite number of steps. A number of numerical experiments in 2d and 3d yield quasi-optimal meshes along with a competitive performance.

Keywords: A posteriori error estimators, data oscillation, adaptive mesh refinement, convergence, performance, quasi-optimal meshes

AMS Subject Classifications: 65N12, 65N15, 65N30, 65N50, 65Y20


Published: SIAM Journal on Numerical Analysis, Volume 38, Number 2 (2000), 466-488.