On a modified Hilbert transformation, the discrete inf-sup condition, and error estimates
<|reference_start|>On a modified Hilbert transformation, the discrete inf-sup condition, and error estimates: In this paper, we analyze the discrete inf-sup condition and related error estimates for a modified Hilbert transformation as used in the space-time discretization of time-dependent partial differential equations. It turns out that the stability constant depends linearly on the finite element mesh parameter, but in most cases, we can show optimal convergence. We present a series of numerical experiments which illustrate the theoretical findings.<|reference_end|>
@article{löscher2024on,
    title={On a modified Hilbert transformation, the discrete inf-sup condition,
  and error estimates},
    author={Richard L"oscher, Olaf Steinbach, Marco Zank},
    journal={arXiv preprint arXiv:2402.08291},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.08291},
    primaryClass={math.NA cs.NA}
}