Finite element approximation for time-dependent diffusion with measure-valued source

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dc.contributor.authorSeidman, Thomas I.
dc.contributor.authorGobbert, Matthias K.
dc.contributor.authorTrott, David W.
dc.contributor.authorKružík, Martin
dc.date.accessioned2018-10-24T16:41:49Z
dc.date.available2018-10-24T16:41:49Z
dc.date.issued2012-06-20
dc.description.abstractThe convergence of finite element methods for elliptic and parabolic partial differential equations is well-established if source terms are sufficiently smooth. Noting that finite element computation is easily implemented even when the source terms are measure-valued—for instance, modeling point sources by Dirac delta distributions—we prove new convergence order results in two and three dimensions both for elliptic and for parabolic equations with measures as source terms. These analytical results are confirmed by numerical tests using COMSOL Multiphysics.en_US
dc.description.sponsorshipThe facility is supported by the U.S. National Science Foundation through the MRI program (Grant no. CNS-0821258) and the SCREMS program (Grant no. DMS-0821311), with additional substantial support from the University of Maryland, Baltimore County (UMBC). See http://www.umbc. edu/hpcf for more information on HPCF and the projects using its resources. M. Kružík was partially supported by the grants IAA 100750802 (GA AV Cˇ R), P201/10/0357, and P105/11/0411 (GA Cˇ R). D. W. Trott also acknowledges financial support as HPCF RA.en_US
dc.description.urihttps://link.springer.com/article/10.1007/s00211-012-0474-8?nullen_US
dc.format.extent15 pagesen_US
dc.genrejournal article pre-printen_US
dc.identifierdoi:10.13016/M20G3H273
dc.identifier.citationSeidman, T.I., Gobbert, M.K., Trott, D.W., Kružík, Martin, Finite Element Approximation for Time-Dependent Diffusion with Measure-Valued Source, Numer. Math. (2012) 122: 709. https://doi.org/10.1007/s00211-012-0474-8en_US
dc.identifier.urihttps://doi.org/10.1007/s00211-012-0474-8
dc.identifier.urihttp://hdl.handle.net/11603/11665
dc.language.isoen_USen_US
dc.publisherSpringer-Verlagen_US
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Mathematics Department Collection
dc.rightsThis item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.
dc.rightsThis is a pre-print of an article published in Numerische Mathematik. The final authenticated version is available online at: https://doi.org/10.1007/s00211-012-0474-8
dc.subjectDirac delta distributionen_US
dc.subjectError estimatesen_US
dc.subjectFinite element approximationen_US
dc.subjectLinear diffusion equationen_US
dc.subjectMeasure-valued dataen_US
dc.subjectUMBC High Performance Computing Facility (HPCF)en_US
dc.titleFinite element approximation for time-dependent diffusion with measure-valued sourceen_US
dc.typeTexten_US

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