# 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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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/s10208-014-9236-6Diening, 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