Local problems on stars: A posteriori error estimators, convergence, and performance
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- by Pedro Morin, Ricardo H. Nochetto and Kunibert G. Siebert HTML | PDF
- Math. Comp. 72 (2003), 1067-1097 Request permission
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.References
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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
- MR Author ID: 131850
- 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
- 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 - © Copyright 2002 American Mathematical Society
- Journal: Math. Comp. 72 (2003), 1067-1097
- MSC (2000): Primary 65N12, 65N15, 65N30, 65N50, 65Y20
- DOI: https://doi.org/10.1090/S0025-5718-02-01463-1
- MathSciNet review: 1972728