Plain convergence of adaptive algorithms without exploiting reliability and efficiency
@article{Gantner2020PlainCO,
title={Plain convergence of adaptive algorithms without exploiting reliability and efficiency},
author={Gregor Gantner and Dirk Praetorius},
journal={ArXiv},
year={2020},
volume={abs/2009.01349}
}
We consider $h$-adaptive algorithms in the context of the finite element method and the boundary element method. Under quite general assumptions on the building blocks SOLVE, ESTIMATE, MARK and REFINE of such algorithms we prove plain convergence in the sense that the adaptive algorithm drives the underlying a posteriori error estimator to zero. Unlike available results in the literature, our analysis avoids the use of any reliability and efficiency estimate but relies only on structural…
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