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arXiv · 1306.0377

Instance optimality of the adaptive maximum strategy

Lars Diening·Christian Kreuzer·Rob Stevenson
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Abstract

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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Lars Diening, Christian Kreuzer, Rob Stevenson. 2014-11-21. Instance optimality of the adaptive maximum strategy. https://doi.org/10.1007/s10208-014-9236-6

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