Lars Diening, Christian Kreuzer, Rob Stevenson
Published 2013-06-03, updated 2014-11-21Version 2
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.
On the Sobolev and $L^p$-Stability of the $L^2$-projection
Grading of Triangulations Generated by Bisection
Constants in Discrete Poincaré and Friedrichs Inequalities and Discrete Quasi-Interpolation
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