Space-Time Isogeometric Method for a Nonlocal Parabolic Problem
<|reference_start|>Space-Time Isogeometric Method for a Nonlocal Parabolic Problem: In the present work, we focus on the space-time isogeometric discretization of a parabolic problem with a nonlocal diffusion coefficient. The use of a space-time discretization with smooth basis functions yields advantages in the approximation of the solution. The existence of the unique solution for continuous and discrete space-time variational formulations is proven. We also establish the a priori error estimate for the space-time isogeometric scheme. The non-linear system is linearized through Picard's method and a suitable preconditioner for the linearized system is provided. Finally, to confirm the theoretical findings, results of some numerical experiments are presented.<|reference_end|>
@article{chaudhary2024space-time,
    title={Space-Time Isogeometric Method for a Nonlocal Parabolic Problem},
    author={Sudhakar Chaudhary, Shreya Chauhan, Monica Montardini},
    journal={arXiv preprint arXiv:2408.00450},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.00450},
    primaryClass={math.NA cs.NA}
}