Finite element approximation for time-dependent diffusion with measure-valued source
| dc.contributor.author | Seidman, Thomas I. | |
| dc.contributor.author | Gobbert, Matthias K. | |
| dc.contributor.author | Trott, David W. | |
| dc.contributor.author | Kružík, Martin | |
| dc.date.accessioned | 2018-10-24T16:41:49Z | |
| dc.date.available | 2018-10-24T16:41:49Z | |
| dc.date.issued | 2012-06-20 | |
| dc.description.abstract | The 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 |
| dc.description.sponsorship | The 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 |
| dc.description.uri | https://link.springer.com/article/10.1007/s00211-012-0474-8?null | en |
| dc.format.extent | 15 pages | en |
| dc.genre | journal article pre-print | en |
| dc.identifier | doi:10.13016/M20G3H273 | |
| dc.identifier.citation | Seidman, 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/s00211-012-0474-8 | en |
| dc.identifier.uri | https://doi.org/10.1007/s00211-012-0474-8 | |
| dc.identifier.uri | http://hdl.handle.net/11603/11665 | |
| dc.language.iso | en | en |
| dc.publisher | Springer-Verlag | en |
| dc.relation.isAvailableAt | The University of Maryland, Baltimore County (UMBC) | |
| dc.relation.ispartof | UMBC Mathematics Department Collection | |
| dc.rights | This 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.rights | This 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.subject | Dirac delta distribution | en |
| dc.subject | Error estimates | en |
| dc.subject | Finite element approximation | en |
| dc.subject | Linear diffusion equation | en |
| dc.subject | Measure-valued data | en |
| dc.subject | UMBC High Performance Computing Facility (HPCF) | en |
| dc.title | Finite element approximation for time-dependent diffusion with measure-valued source | en |
| dc.type | Text | en |