Abstract
We propose and analyze an hp-adaptive DG–FEM algorithm, termed \(\varvec {hp}\)-ADFEM, and its one-dimensional realization, which is convergent, instance optimal, and h- and p-robust. The procedure consists of iterating two routines: one hinges on Binev’s algorithm for the adaptive hp-approximation of a given function, and finds a near-best hp-approximation of the current discrete solution and data to a desired accuracy; the other one improves the discrete solution to a finer but comparable accuracy, by iteratively applying Dörfler marking and h refinement.
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Acknowledgements
Work carried out within the “Progetto di Eccellenza 2018-2022”, granted by MIUR (Italian Ministry of University and Research) to the Department of Mathematical Sciences, Politecnico di Torino. The authors are members of the INdAM research group GNCS, which granted partial support to this research.
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Antonietti, P., Canuto, C. & Verani, M. An Adaptive hp–DG–FE Method for Elliptic Problems: Convergence and Optimality in the 1D Case. Commun. Appl. Math. Comput. 1, 309–331 (2019). https://doi.org/10.1007/s42967-019-00026-9
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DOI: https://doi.org/10.1007/s42967-019-00026-9