{"_id":"53140","user_id":"100441","language":[{"iso":"eng"}],"date_created":"2024-04-03T09:08:38Z","doi":"10.48550/ARXIV.2312.05511","date_updated":"2024-04-03T09:12:47Z","year":"2023","type":"journal_article","abstract":[{"lang":"eng","text":"We present a new stability and error analysis of fully discrete approximation schemes for the transient Stokes equation. For the spatial discretization, we consider a wide class of Galerkin finite element methods which includes both inf-sup stable spaces and symmetric pressure stabilized formulations. We extend the results from Burman and Fernández [\\textit{SIAM J. Numer. Anal.}, 47 (2009), pp. 409-439] and provide a unified theoretical analysis of backward difference formulae (BDF methods) of order 1 to 6. The main novelty of our approach lies in the use of Dahlquist's G-stability concept together with multiplier techniques introduced by Nevannlina-Odeh and recently by Akrivis et al. [\\textit{SIAM J. Numer. Anal.}, 59 (2021), pp. 2449-2472] to derive optimal stability and error estimates for both the velocity and the pressure. When combined with a method dependent Ritz projection for the initial data, unconditional stability can be shown while for arbitrary interpolation, pressure stability is subordinate to the fulfillment of a mild inverse CFL-type condition between space and time discretizations."}],"publication":"arXiv","department":[{"_id":"841"}],"citation":{"chicago":"Contri, Alessandro, Balázs Kovács, and André Massing. “Error Analysis of BDF 1-6 Time-Stepping Methods for the Transient Stokes Problem: Velocity and Pressure Estimates.” <i>ArXiv</i>, 2023. <a href=\"https://doi.org/10.48550/ARXIV.2312.05511\">https://doi.org/10.48550/ARXIV.2312.05511</a>.","ieee":"A. Contri, B. Kovács, and A. Massing, “Error analysis of BDF 1-6 time-stepping methods for the transient Stokes problem: velocity and pressure estimates,” <i>arXiv</i>, 2023, doi: <a href=\"https://doi.org/10.48550/ARXIV.2312.05511\">10.48550/ARXIV.2312.05511</a>.","bibtex":"@article{Contri_Kovács_Massing_2023, title={Error analysis of BDF 1-6 time-stepping methods for the transient Stokes problem: velocity and pressure estimates}, DOI={<a href=\"https://doi.org/10.48550/ARXIV.2312.05511\">10.48550/ARXIV.2312.05511</a>}, journal={arXiv}, author={Contri, Alessandro and Kovács, Balázs and Massing, André}, year={2023} }","ama":"Contri A, Kovács B, Massing A. Error analysis of BDF 1-6 time-stepping methods for the transient Stokes problem: velocity and pressure estimates. <i>arXiv</i>. Published online 2023. doi:<a href=\"https://doi.org/10.48550/ARXIV.2312.05511\">10.48550/ARXIV.2312.05511</a>","mla":"Contri, Alessandro, et al. “Error Analysis of BDF 1-6 Time-Stepping Methods for the Transient Stokes Problem: Velocity and Pressure Estimates.” <i>ArXiv</i>, 2023, doi:<a href=\"https://doi.org/10.48550/ARXIV.2312.05511\">10.48550/ARXIV.2312.05511</a>.","apa":"Contri, A., Kovács, B., &#38; Massing, A. (2023). Error analysis of BDF 1-6 time-stepping methods for the transient Stokes problem: velocity and pressure estimates. <i>ArXiv</i>. <a href=\"https://doi.org/10.48550/ARXIV.2312.05511\">https://doi.org/10.48550/ARXIV.2312.05511</a>","short":"A. Contri, B. Kovács, A. Massing, ArXiv (2023)."},"status":"public","author":[{"full_name":"Contri, Alessandro","last_name":"Contri","first_name":"Alessandro"},{"last_name":"Kovács","full_name":"Kovács, Balázs","orcid":"0000-0001-9872-3474","id":"100441","first_name":"Balázs"},{"last_name":"Massing","full_name":"Massing, André","first_name":"André"}],"title":"Error analysis of BDF 1-6 time-stepping methods for the transient Stokes problem: velocity and pressure estimates"}