Optimal error estimates of the penalty finite element method for the unsteady Navier-Stokes equations with nonsmooth initial data

[2202.03777] Optimal error estimates of the penalty finite element method for the unsteady Navier-Stokes equations with nonsmooth initial data Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Numerical Analysis arXiv:2202.03777 (math) [Submitted on 8 Feb 2022 ( v1 ), last revised 11 Jul 2023 (this version, v2)] Title: Optimal error estimates of the penalty finite element method for the unsteady Navier-Stokes equations with nonsmooth initial data Authors: Bikram Bir , Deepjyoti Goswami , Amiya K. Pani View a PDF of the paper titled Optimal error estimates of the penalty finite element method for the unsteady Navier-Stokes equations with nonsmooth initial data, by Bikram Bir and 1 other authors View PDF HTML (experimental) Abstract: In this paper, both semidiscrete and fully discrete finite element methods are analyzed for the penalized two-dimensional unsteady Navier-Stokes equations with nonsmooth initial data. First order backward Euler method is applied for the time discretization, whereas conforming finite element method is used for the spatial discretization. Optimal $L^2$ error estimates for the semidiscrete as well as the fully discrete approximations of the velocity and of the pressure are derived for realistically assumed conditions on the data. The main ingredient in the proof is the appropriate exploitation of the inverse of the penalized Stokes operator, negative norm estimates and time weighted estimates. Numerical examples are discussed at the end which conform our theoretical results. Comments: 31 pages, 11 figures Subjects: Numerical Analysis (math.NA) MSC classes: 65M60, 65M15, 35Q35 Cite as: arXiv:2202.03777 [math.NA] (or arXiv:2202.03777v2 [math.NA] for this version) https://doi.org/10.48550/arXiv.2202.03777 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1007/s10915-023-02445-6 Focus to learn more DOI(s) linking to related resources Submission history From: Bikram Bir [ view email ] [v1] Tue, 8 Feb 2022 10:46:53 UTC (63 KB) [v2] Tue, 11 Jul 2023 10:45:41 UTC (526 KB) Full-text links: Access Paper: View a PDF of the paper titled Optimal error estimates of the penalty finite element method for the unsteady Navier-Stokes equations with nonsmooth initial data, by Bikram Bir and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.NA < prev | next > new | recent | 2022-02 Change to browse by: cs cs.NA math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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