A parallel adaptive space-time discontinuousGalerkin method for transport in porous media

A parallel adaptive space-time discontinuousGalerkin method for transport in porous media | 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 A parallel adaptive space-time discontinuousGalerkin method for transport in porous media Daniele Corallo, Christian Wieners This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6347510/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 22 Sep, 2025 Read the published version in GEM - International Journal on Geomathematics → Version 1 posted You are reading this latest preprint version Abstract We introduce a parallel adaptive space-time discontinuous Galerkin method for the linear transport equation, where the transport vector is determined from the porous media equation. Given the permeability distribution, in the first step the pressure head and the flux is computed by a mixed approximation of the linear porous media problem. Then, for a given initial pollution distribution the linear transport is approximated by an adaptive DG space-time discretization which turns out to be very efficient since the adaptively refined region is transported with the pollution distribution. The full linear system in space and time is solved with a multigrid method. Finally we apply this method to solve the inverse problem to reconstruct the initial pollution distribution from measurements of the outflow. space-time methods discontinuous Galerkin discretization linear transport in porous media Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 22 Sep, 2025 Read the published version in GEM - International Journal on Geomathematics → 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. 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-6347510","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":454940118,"identity":"cf1881f0-410e-4d72-91c1-224f5e09208c","order_by":0,"name":"Daniele Corallo","email":"","orcid":"","institution":"KIT","correspondingAuthor":false,"prefix":"","firstName":"Daniele","middleName":"","lastName":"Corallo","suffix":""},{"id":454940119,"identity":"7799471e-3f99-4df6-906c-2a0ab0ae2ba1","order_by":1,"name":"Christian Wieners","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/0lEQVRIie3PMWrDMBTG8WcC7aLgVVCCr/CCh7TgpleRMahj10zFkzqlc00voTHZnhHEiw8QaJcunZ3NGUqqaGkzyFkz6D8YIfzDnwFCoUuMA5B7gjvYrpU7ROUgEf8J2wDRGQIgTm6kw14Svy+/6n1/m8yATWm3yp6S6js3HWQTTZ6PfDZomODTdcmwrlp5pz8k2WEy9RG0M4z9l0jTWJuxMog3j6UlJh8idS/4gyM/6oBJ1RzJYZCQHZY7EilC2F4dh5GX8K0dxiQvtIm7eqkKxFYKarFIKw+J3+Ro12fP97pRRbdXc0xeNmm3WMwnrx7y1+h08LnXQ6FQKDTUL1rYaYaeofh6AAAAAElFTkSuQmCC","orcid":"","institution":"KIT","correspondingAuthor":true,"prefix":"","firstName":"Christian","middleName":"","lastName":"Wieners","suffix":""}],"badges":[],"createdAt":"2025-03-31 19:53:06","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6347510/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6347510/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s13137-025-00273-4","type":"published","date":"2025-09-22T15:57:24+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":92430591,"identity":"a06dca83-b077-4287-b6ad-ed24f0d9944c","added_by":"auto","created_at":"2025-09-29 16:06:28","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":920956,"visible":true,"origin":"","legend":"","description":"","filename":"GEMSpaceTimeTransport.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6347510/v1_covered_f49f5106-fd16-4df5-80b8-95855c601e09.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A parallel adaptive space-time discontinuousGalerkin method for transport in porous media","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":true,"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":"space-time methods, discontinuous Galerkin discretization, linear transport in porous media","lastPublishedDoi":"10.21203/rs.3.rs-6347510/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6347510/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We introduce a parallel adaptive space-time discontinuous Galerkin method for the linear transport equation, where the transport vector is determined from the porous media equation. 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