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Abstract In this paper, optimal convergence for an adaptive finite element algorithm for elastoplasticity is considered. To this end, the proposed adaptive algorithm is established within the abstract framework of the axioms of adaptivity C. Carstensen, M. Feischl, M. Page and D. Praetorius, Axioms of adaptivity, Comput. Math. Appl. 67 2014, 6, 1195–1253, which provides a specific proceeding to prove the optimal convergence of the scheme. The proceeding is based on verifying four axioms, which ensure the optimal convergence. The verification is done by using results from C. Carstensen, A. Schröder and S. Wiedemann, An optimal adaptive finite element method for elastoplasticity, Numer. Math. 132 2016, 1, 131–154, which presents an alternative approach to optimality without explicitly relying on the axioms
Schönauer et al. (2024) studied this question.