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arXiv · 2208.10143

Plain convergence of goal-oriented adaptive FEM

Valentin Helml·Michael Innerberger·Dirk Praetorius
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Abstract

We discuss goal-oriented adaptivity in the frame of conforming finite element methods and plain convergence of the related a posteriori error estimator for different general marking strategies. We present an abstract analysis for two different settings. First, we consider problems where a local discrete efficiency estimate holds. Second, we show plain convergence in a setting that relies only on structural properties of the error estimators, namely stability on non-refined elements as well as reduction on refined elements. In particular, the second setting does not require reliability and efficiency estimates. Numerical experiments underline our theoretical findings.

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Valentin Helml, Michael Innerberger, Dirk Praetorius. 2022-08-22. Plain convergence of goal-oriented adaptive FEM. https://doi.org/10.1016/j.camwa.2023.07.022

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