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

Math. Comp., 72 (2003), 1067--1097.

Pedro Morin
Instituto de Matematica Aplicada del Litoral
Guemes 3450
3000 Santa Fe, Argentina


Ricardo H. Nochetto
Department of Mathematics
University of Maryland, College Park
College Park, MD 20742, USA


Kunibert G. Siebert
Institut fuer Angewandte Mathematik
Hermann-Herder-Str. 10
79104 Freiburg, Germany



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.