# 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.

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Journal Article | Published | English

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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.
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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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arXiv 1306.0377