A Variational Finite Element Method for Source Inversion for Convective-Diffusive Transport

dc.contributor.authorAkçelik, Volkan
dc.contributor.authorBiros, George
dc.contributor.authorGhattas, Omar
dc.contributor.authorLong, Kevin R.
dc.contributor.authorvan Bloemen Waanders, Bart
dc.date2023-05-16T23:37:01.000
dc.date.accessioned2023-05-22T23:51:02Z
dc.date.available2023-05-22T23:51:02Z
dc.date.issued2003-05-01
dc.date.submitted2006-01-23T09:18:36-08:00
dc.description.abstractWe consider the inverse problem of determining an arbitrary source in a time-dependent convective-diffusive transport equation, given a velocity field and pointwise measurements of the concentration. Applications that give rise to such problems include determination of groundwater or airborne pollutant sources from measurements of concentrations, and identification of sources of chemical or biological attacks. To address ill-posedness of the problem, we employ Tikhonov and total variation regularization. We present a variational formulation of the first order optimality system, which includes the initial-boundary value state problem, the final-boundary value adjoint problem, and the space-time boundary value source problem. We discretize in the space-time volume using Galerkin finite elements. Several examples demonstrate the influence of the density of the sensor array, the effectiveness of total variation regularization for discontinuous sources, the invertibility of the source as the transport becomes increasingly convection-dominated, the ability of the space-time inversion formulation to track moving sources, and the optimal convergence rate of the finite element approximation.
dc.description.commentsPostprint version. Published in Finite Elements in Analysis and Design, Volume 39, Issue 8, May 2003, pages 683-705. Publisher URL: http://dx.doi.org/10.1016/S0168-874X(03)00054-4 NOTE: At the time of publication, author George Biros was affiliated with New York University. Currently (January 2006), he is a faculty member in the Department of Mechanical Engineering and Applied Mechanics at the University of Pennsylvania.
dc.identifier.urihttps://repository.upenn.edu/handle/20.500.14332/40068
dc.legacy.articleid1063
dc.legacy.fulltexturlhttps://repository.upenn.edu/cgi/viewcontent.cgi?article=1063&context=meam_papers&unstamped=1
dc.source.issue63
dc.source.journalDepartmental Papers (MEAM)
dc.source.peerreviewedtrue
dc.source.statuspublished
dc.titleA Variational Finite Element Method for Source Inversion for Convective-Diffusive Transport
dc.typeArticle
digcom.identifiermeam_papers/63
digcom.identifier.contextkey136067
digcom.identifier.submissionpathmeam_papers/63
digcom.typearticle
dspace.entity.typePublication
relation.isAuthorOfPublicationfa648fa1-4879-41c5-ad3c-540b2ee6eceb
relation.isAuthorOfPublication.latestForDiscoveryfa648fa1-4879-41c5-ad3c-540b2ee6eceb
upenn.schoolDepartmentCenterDepartmental Papers (MEAM)
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