Helml, V., Innerberger, M., & Praetorius, D. (2023). Plain convergence of goal-oriented adaptive FEM. Computers and Mathematics with Applications, 147, 130–149. https://doi.org/10.1016/j.camwa.2023.07.022
Adaptivity; Convergence; Finite element method; Goal-oriented algorithm
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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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Project title:
Doktoratskolleg "Dissipation and Dispersion in Nonlinear Partial Differential Equations": W1245-N25 (FWF Fonds zur Förderung der wissenschaftlichen Forschung (FWF)) Analytische und numerische Koppelung im Mikromagnetismus: F 6509-N36 (FWF Fonds zur Förderung der wissenschaftlichen Forschung (FWF)) Computational nonlinear PDEs: P 33216-N (FWF Fonds zur Förderung der wissenschaftlichen Forschung (FWF))
