Local problems on stars: a posteriori error estimators, convergence, and performance

Authors:
Pedro Morin;Ricardo H. Nochetto;Kunibert G. Siebert
Affiliations:
Departamento de Matemática, Facultad de Ingeniería Química, Universidad Nacional del Litoral, Santiago del Estero 2829, 3000 Santa Fe, Argentina;Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland;Institut für Angewandte Mathematik, Hermann-Herder-Str. 10, 79104 Freiburg, Germany
Venue:
Mathematics of Computation
Year:
2003

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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 pre-adaptation nor explicit knowledge of constants. Numerical experiments reveal a competitive performance, show extremely good effectivity indices, and yield quasi-optimal meshes.