Instance optimality of the adaptive maximum strategy

Diening L, Kreuzer C, Stevenson R (2016)
Foundations of Computational Mathematics. The Journal of the Society for the Foundations of Computational Mathematics 16(1): 33-68.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
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Autor*in
Diening, LarsUniBi ; Kreuzer, Christian; Stevenson, Rob
Abstract / Bemerkung
In this paper, we prove that the standard adaptive finite element method with a (modified) `maximum marking strategy' is `instance optimal' for the `total error', being the sum of the energy error and the oscillation. This result will be derived in the model setting of Poisson's equation on a polygon, linear finite elements, and conforming triangulations created by newest vertex bisection.
Erscheinungsjahr
2016
Zeitschriftentitel
Foundations of Computational Mathematics. The Journal of the Society for the Foundations of Computational Mathematics
Band
16
Ausgabe
1
Seite(n)
33-68
ISSN
1615-3375
Page URI
https://pub.uni-bielefeld.de/record/2913491

Zitieren

Diening L, Kreuzer C, Stevenson R. Instance optimality of the adaptive maximum strategy. Foundations of Computational Mathematics. The Journal of the Society for the Foundations of Computational Mathematics. 2016;16(1):33-68.
Diening, L., Kreuzer, C., & Stevenson, R. (2016). Instance optimality of the adaptive maximum strategy. Foundations of Computational Mathematics. The Journal of the Society for the Foundations of Computational Mathematics, 16(1), 33-68. doi:10.1007/s10208-014-9236-6
Diening, L., Kreuzer, C., and Stevenson, R. (2016). Instance optimality of the adaptive maximum strategy. Foundations of Computational Mathematics. The Journal of the Society for the Foundations of Computational Mathematics 16, 33-68.
Diening, L., Kreuzer, C., & Stevenson, R., 2016. Instance optimality of the adaptive maximum strategy. Foundations of Computational Mathematics. The Journal of the Society for the Foundations of Computational Mathematics, 16(1), p 33-68.
L. Diening, C. Kreuzer, and R. Stevenson, “Instance optimality of the adaptive maximum strategy”, Foundations of Computational Mathematics. The Journal of the Society for the Foundations of Computational Mathematics, vol. 16, 2016, pp. 33-68.
Diening, L., Kreuzer, C., Stevenson, R.: Instance optimality of the adaptive maximum strategy. Foundations of Computational Mathematics. The Journal of the Society for the Foundations of Computational Mathematics. 16, 33-68 (2016).
Diening, Lars, Kreuzer, Christian, and Stevenson, Rob. “Instance optimality of the adaptive maximum strategy”. Foundations of Computational Mathematics. The Journal of the Society for the Foundations of Computational Mathematics 16.1 (2016): 33-68.

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