Error estimates for full discretization of Cahn--Hilliard equation with dynamic boundary conditions
<|reference_start|>Error estimates for full discretization of Cahn--Hilliard equation with dynamic boundary conditions: A proof of optimal-order error estimates is given for the full discretization of the Cahn--Hilliard equation with Cahn--Hilliard-type dynamic boundary conditions in a smooth domain. The numerical method combines a linear bulk--surface finite element discretization in space and linearly implicit backward difference formulae of order 1 to 5 in time. Optimal-order error estimates are proven. The error estimates are based on a consistency and stability analysis in an abstract framework, based on energy estimates exploiting the anti-symmetric structure of the second-order system.<|reference_end|>
@article{bullerjahn2024error,
    title={Error estimates for full discretization of Cahn--Hilliard equation with
  dynamic boundary conditions},
    author={Nils Bullerjahn, Bal'azs Kov'acs},
    journal={arXiv preprint arXiv:2407.20698},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.20698},
    primaryClass={math.NA cs.NA}
}