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arXiv · 1402.3959

Robust Localization of the Best Error with Finite Elements in the Reaction-Diffusion Norm

Francesca Tantardini·Andreas Veeser·R"udiger Verf"urth
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Abstract

We consider the approximation in the reaction-diffusion norm with continuous finite elements and prove that the best error is equivalent to a sum of the local best errors on pairs of elements. The equivalence constants do not depend on the ratio of diffusion to reaction. As application, we derive local error functionals that ensure robust performance of adaptive tree approximation in the reaction-diffusion norm.

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Francesca Tantardini, Andreas Veeser, R"udiger Verf"urth. 2014-02-17. Robust Localization of the Best Error with Finite Elements in the Reaction-Diffusion Norm. https://doi.org/10.1007/s00365-015-9291-5

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