The mixed virtual element method with optimal convergence for the semiconductor device problem

The mixed virtual element method with optimal convergence for the semiconductor device problem | 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 The mixed virtual element method with optimal convergence for the semiconductor device problem XIndong Li, Wenwen Xu, LU Yang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4679621/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This paper is concerned with the virtual element method for the semiconductor device problem on polygonal meshes. Specifically, The potential equation is discretized by the mixed virtual element method and the electron and hole density equations by the original virtual element method. The optimal convergence analysis of the numerical solutions for the electrostatic potential, the electric field intensity, the electron density and the hole density is carried out for full discrete scheme. The validity and stability of the method are verified by numerical experiments. mixed virtual element method the semiconductor device optimal error estimates polygonal meshes Full Text Additional Declarations No competing interests reported. Supplementary Files VEMsemiconductorNA.rar Cite Share Download PDF Status: Posted Version 1 posted 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. 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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-4679621","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":334341767,"identity":"b9281438-48d0-44f6-b2ef-9c832f306981","order_by":0,"name":"XIndong Li","email":"","orcid":"","institution":"Qilu University of Technology","correspondingAuthor":false,"prefix":"","firstName":"XIndong","middleName":"","lastName":"Li","suffix":""},{"id":334341770,"identity":"b770d5d2-ae90-4780-bede-7bfb07076a62","order_by":1,"name":"Wenwen Xu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4UlEQVRIiWNgGAWjYDADNvbmgw8+GNjYEa+Fn+dYsuGMgrRk4rVIzsgxk+b5cIixgZBKgxs5ho8L22zyDG4kGEjbGBxgZmA/fHQDAcONjWe2pRUbnHmQYJxjcIePgSct7QZeL0jkbpPm3XY4ccPxhAPJOQbPmBkkeMzwamGTyN3+m3fb/8QNBxIbDlsYHGZsIKQFZAsz77YDiTM7khmbGYjRItnz/rM077/kxH6eY8yMPQZpyWyE/GJwPC3xM88Zu8Q29v7vP378sbHjZz98DK8WLL4jTfkoGAWjYBSMAmwAAClUTYbRK0N6AAAAAElFTkSuQmCC","orcid":"","institution":"Qilu University of Technology","correspondingAuthor":true,"prefix":"","firstName":"Wenwen","middleName":"","lastName":"Xu","suffix":""},{"id":334341772,"identity":"108953c9-84d6-4a4e-b556-00d018a3cc8f","order_by":2,"name":"LU Yang","email":"","orcid":"","institution":"Qilu University of Technology","correspondingAuthor":false,"prefix":"","firstName":"LU","middleName":"","lastName":"Yang","suffix":""}],"badges":[],"createdAt":"2024-07-03 10:21:02","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4679621/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4679621/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":80427057,"identity":"ba50a164-59c4-431b-b1a3-2e9afb0f8466","added_by":"auto","created_at":"2025-04-11 22:16:30","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":666075,"visible":true,"origin":"","legend":"","description":"","filename":"VEMsemiconductor.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4679621/v1_covered_7e7567a8-be18-4279-b040-187776c53fab.pdf"},{"id":61614895,"identity":"dfe77f63-b3b0-4290-9989-8315f20d0bd4","added_by":"auto","created_at":"2024-08-02 02:54:19","extension":"rar","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":2466455,"visible":true,"origin":"","legend":"","description":"","filename":"VEMsemiconductorNA.rar","url":"https://assets-eu.researchsquare.com/files/rs-4679621/v1/5e5668976c646d6b5b0b1424.rar"}],"financialInterests":"No competing interests reported.","formattedTitle":"The mixed virtual element method with optimal convergence for the semiconductor device problem","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"mixed virtual element method, the semiconductor device, optimal error estimates, polygonal meshes","lastPublishedDoi":"10.21203/rs.3.rs-4679621/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4679621/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This paper is concerned with the virtual element method for the semiconductor device problem on polygonal meshes. 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