Robust a posteriori error control for the Allen-Cahn equation with variable mobility
<|reference_start|>Robust a posteriori error control for the Allen-Cahn equation with variable mobility: In this work, we derive a $\gamma$-robust a posteriori error estimator for finite element approximations of the Allen-Cahn equation with variable non-degenerate mobility. The estimator utilizes spectral estimates for the linearized steady part of the differential operator as well as a conditional stability estimate based on a weighted sum of Bregman distances, based on the energy and a functional related to the mobility. A suitable reconstruction of the numerical solution in the stability estimate leads to a fully computable estimator.<|reference_end|>
@article{brunk2024robust,
    title={Robust a posteriori error control for the Allen-Cahn equation with
  variable mobility},
    author={Aaron Brunk, Jan Giesselmann, Maria Lukacova-Medvidova},
    journal={arXiv preprint arXiv:2403.08898},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.08898},
    primaryClass={math.NA cs.NA math.AP}
}