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Optimal AFEM convergence for any bulk parameter smaller than one
Abstract
We prove rate-optimal convergence of the standard adaptive finite element method with conforming Lagrange elements for the Poisson problem for Dörfler marking with any bulk parameter θ∈ (0,1). This removes the smallness restriction on the bulk parameter that has persisted in the classical theory of optimal adaptive finite element methods.
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BibTeX
@misc{diening2026optimal,
title = {{Optimal AFEM convergence for any bulk parameter smaller than one}},
author = {Lars Diening and Johannes Storn},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39719},
eprint = {2610.39719},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39719},
}
RIS
TY - UNPB
TI - Optimal AFEM convergence for any bulk parameter smaller than one
AU - Lars Diening
AU - Johannes Storn
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39719
UR - https://arxiv.org/abs/2610.39719
AB - We prove rate-optimal convergence of the standard adaptive finite element method with conforming Lagrange elements for the Poisson problem for Dörfler marking with any bulk parameter θ∈ (0,1). This removes the smallness restriction on the bulk parameter that has persisted in the classical theory of optimal adaptive finite element methods.
ER -