A nonnegativity-preserving finite element method for a class of parabolic SPDEs with multiplicative noise

[2502.16854] A nonnegativity-preserving finite element method for a class of parabolic SPDEs with multiplicative noise Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Numerical Analysis arXiv:2502.16854 (math) [Submitted on 24 Feb 2025 ( v1 ), last revised 9 Feb 2026 (this version, v2)] Title: A nonnegativity-preserving finite element method for a class of parabolic SPDEs with multiplicative noise Authors: Ana Djurdjevac , Claude Le Bris , Endre Süli View a PDF of the paper titled A nonnegativity-preserving finite element method for a class of parabolic SPDEs with multiplicative noise, by Ana Djurdjevac and 1 other authors View PDF HTML (experimental) Abstract: We consider a prototypical parabolic SPDE with finite-dimensional multiplicative noise, which, subject to a nonnegative initial datum, has a unique nonnegative solution. Inspired by well-established techniques in the deterministic case, we introduce a finite element discretization of this SPDE that is convergent and which, subject to a nonnegative initial datum and unconditionally with respect to the spatial discretization parameter, preserves nonnegativity of the numerical solution throughout the course of evolution. We perform a mathematical analysis of this method. In addition, in the associated linear setting, we develop a fully discrete scheme that also preserves nonnegativity, and we present numerical experiments that illustrate the advantages of the proposed method over alternative finite element and finite difference methods that were previously considered in the literature, which do not necessarily guarantee nonnegativity of the numerical solution. Subjects: Numerical Analysis (math.NA) MSC classes: 65M60, 60H35, 60H15 ACM classes: G.1.8; G.3 Cite as: arXiv:2502.16854 [math.NA] (or arXiv:2502.16854v2 [math.NA] for this version) https://doi.org/10.48550/arXiv.2502.16854 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1007/s40072-026-00423-1 Focus to learn more DOI(s) linking to related resources Submission history From: Ana Djurdjevac [ view email ] [v1] Mon, 24 Feb 2025 05:30:17 UTC (331 KB) [v2] Mon, 9 Feb 2026 08:57:56 UTC (330 KB) Full-text links: Access Paper: View a PDF of the paper titled A nonnegativity-preserving finite element method for a class of parabolic SPDEs with multiplicative noise, by Ana Djurdjevac and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.NA < prev | next > new | recent | 2025-02 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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