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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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


Authors: Pedro Morin, Ricardo H. Nochetto and Kunibert G. Siebert
Journal: Math. Comp. 72 (2003), 1067-1097
MSC (2000): Primary 65N12, 65N15, 65N30, 65N50, 65Y20
Published electronically: November 7, 2002
MathSciNet review: 1972728
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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.


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Additional Information

Pedro Morin
Affiliation: Departamento de Matemática, Facultad de Ingeniería Química, Universidad Nacional del Litoral, Santiago del Estero 2829, 3000 Santa Fe, Argentina
Email: pmorin@math.unl.edu.ar

Ricardo H. Nochetto
Affiliation: Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742
Email: rhn@math.umd.edu

Kunibert G. Siebert
Affiliation: Institut für Angewandte Mathematik, Hermann-Herder-Str. 10, 79104 Freiburg, Germany
Email: kunibert@mathematik.uni-freiburg.de

DOI: http://dx.doi.org/10.1090/S0025-5718-02-01463-1
PII: S 0025-5718(02)01463-1
Keywords: A posteriori error estimators, local problems, stars, data oscillation, adaptivity, convergence, performance
Received by editor(s): October 12, 2000
Received by editor(s) in revised form: September 26, 2001
Published electronically: November 7, 2002
Additional Notes: The first author was partially supported by CONICET of Argentina, NSF Grant DMS-9971450, and NSF/DAAD Grant INT-9910086. This work was developed while this author was visiting the University of Maryland
The second author was partially supported by NSF Grant DMS-9971450 and NSF/DAAD Grant INT-9910086
The third author was partially suported by DAAD/NSF grant “Projektbezogene Förderung des Wissenschaftleraustauschs in den Natur-, Ingenieur- und den Sozialwissenschaften mit der NSF”. Part of this work was developed while this author was visiting the University of Maryland
Article copyright: © Copyright 2002 American Mathematical Society