Damped energy-norm a posteriori error estimates for fully discrete approximations of the wave equation using C2-reconstructions
<|reference_start|>Damped energy-norm a posteriori error estimates for fully discrete approximations of the wave equation using C2-reconstructions: We derive a posteriori error estimates for the the scalar wave equation discretized in space by continuous finite elements and in time by the explicit leapfrog scheme. Our analysis combines the idea of invoking extra time-regularity for the right-hand side, as previously introduced in the space semi-discrete setting, with a novel, piecewise quartic, globally twice-differentiable time-reconstruction of the fully discrete solution. Our main results show that the proposed estimator is reliable and efficient in a damped energy norm. These properties are illustrated in a series of numerical examples.<|reference_end|>
@article{chaumont-frelet2024damped,
    title={Damped energy-norm a posteriori error estimates for fully discrete
  approximations of the wave equation using C2-reconstructions},
    author={T. Chaumont-Frelet and A. Ern},
    journal={arXiv preprint arXiv:2403.12954},
    year={2024},
    number={hal-04511867},
    archivePrefix={arXiv},
    eprint={2403.12954},
    primaryClass={math.NA cs.NA}
}