Local Problems on Stars: A Posteriori Error Estimators, Convergence, and Performance

Abstract

A new computable a posteriori error estimator is introduced, which relies on the solution of small discrete problems on stars. It exhibits built-in flux equilibration and is equivalent to the energy error up to data oscillation without any saturation assumption. A simple adaptive strategy is designed, which simultaneously reduces error and data oscillation, and is shown to converge without mesh preadaptation nor explicit knowledge of constants. Numerical experiments reveal a competitive performance, show extremely good effectivity indices, and yield quasi-optimal meshes.

Keywords: A posteriori error estimators, local problems, stars, data oscillation, adaptivity, convergence, performance

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


Published: Mathematics of Computation 72 (2003), 1067-1097.