Convergence of a high order method in time and space for the miscible displacement equations

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dc.citation.firstpage953
dc.citation.issueNumber4
dc.citation.journalTitleESAIM: M2AN
dc.citation.lastpage976
dc.citation.volumeNumber49
dc.contributor.authorLi, Jizhou
dc.contributor.authorRiviere, Beatrice
dc.contributor.authorWalkington, Noel
dc.date.accessioned2016-02-02T19:17:44Z
dc.date.available2016-02-02T19:17:44Z
dc.date.issued2015
dc.description.abstractA numerical method is formulated and analyzed for solving the miscible displacement problem under low regularity assumptions. The scheme employs discontinuous Galerkin time stepping with mixed and interior penalty discontinuous Galerkin finite elements in space. The numerical approximations of the pressure, velocity, and concentration converge to the weak solution as the mesh size and time step tend to zero. To pass to the limit a compactness theorem is developed which generalizes the Aubin-Lions theorem to accommodate discontinuous functions both in space and in time.
dc.identifier.citationLi, Jizhou, Riviere, Beatrice and Walkington, Noel. "Convergence of a high order method in time and space for the miscible displacement equations." <i>ESAIM: M2AN,</i> 49, no. 4 (2015) EDP Sciences: 953-976. http://dx.doi.org/10.1051/m2an/2014059.
dc.identifier.doihttp://dx.doi.org/10.1051/m2an/2014059
dc.identifier.urihttps://hdl.handle.net/1911/88306
dc.language.isoeng
dc.publisherEDP Sciences
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
dc.subject.keywordGeneralized Aubin-Lions
dc.subject.keyworddiscontinuous Galerkin
dc.subject.keywordmixed finite element
dc.subject.keywordarbitrary order
dc.subject.keywordweak solution
dc.subject.keywordconvergence
dc.titleConvergence of a high order method in time and space for the miscible displacement equations
dc.typeJournal article
dc.type.dcmiText
dc.type.publicationpublisher version
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