Simple Positivity Preserving Nonlinear Finite Volume Scheme for Subdiffusion Equations on General Non-conforming Distorted Meshes

Simple Positivity Preserving Nonlinear Finite Volume Scheme for Subdiffusion Equations on General Non-conforming Distorted Meshes | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Simple Positivity Preserving Nonlinear Finite Volume Scheme for Subdiffusion Equations on General Non-conforming Distorted Meshes Xuehua Yang, Haixiang Zhang, Qi Zhang, Guangwei Yuan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-432959/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 04 Apr, 2022 Read the published version in Nonlinear Dynamics → Version 1 posted 5 You are reading this latest preprint version Abstract We propose a positivity preserving finite volume scheme on non-conforming quadrilateral distorted meshes with hanging nodes for subdiffusion equations, where the differential equations have a sum of time-fractional derivatives of different orders, and the typical solutions of the problem have a weak singularity at the initial time t =0 for given smooth data. In this paper, a positivity-preserving nonlinear method with centered unknowns is obtained by the two point flux technique, where a new method to handling vertex-unknown including hanging nodes is the highlight of our paper. For each time derivative, we apply the L1 scheme on a temporal graded mesh. Especially, the existence of a solution is strictly proved for the nonlinear system by applying the Brouwer’s fixed point theorem. Numerical results show that the proposed positivity-preserving method is effective for strongly anisotropic and heterogeneous full tensor subdiffusion coefficient problems. Mathematical and Theoretical Biology Time fractional subdiffusion equation L1 scheme Positivity-preserving Non-conforming Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 Full-Text Due to technical limitations, full-text HTML conversion of this manuscript could not be completed. However, the manuscript can be downloaded and accessed as a PDF. Cite Share Download PDF Status: Published Journal Publication published 04 Apr, 2022 Read the published version in Nonlinear Dynamics → Version 1 posted Editorial decision: Minor revisions 02 Jul, 2021 Reviews received at journal 25 May, 2021 Reviewers invited by journal 25 May, 2021 First submitted to journal 15 Apr, 2021 Editor assigned by journal 15 Apr, 2021 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-432959","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":29492425,"identity":"0981a491-790e-4a84-adb5-d3f38acb4941","order_by":0,"name":"Xuehua 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