FEM Convergence for PDEs with Point Sources in 2-D and 3-D

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dc.contributor.authorGobbert, M.
dc.contributor.authorKalayeh, K. M.
dc.contributor.authorGraf, J. S.
dc.date.accessioned2018-10-15T14:12:10Z
dc.date.available2018-10-15T14:12:10Z
dc.date.issued2015
dc.descriptionCOMSOL Conference 2015, Boston, MA.en_US
dc.description.abstractNumerical theory provides the basis for quantification of the accuracy and reliability of a FEM solution by error estimates on the FEM error vs. the mesh spacing of the FEM mesh. This paper presents techniques needed in COMSOL 5.1 to perform computational studies for elliptic test problems in two and three space dimensions that demonstrate this theory by computing the convergence order of the FEM error. In particular, we show how to perform these techniques for a problem involving a point source modeled by a Dirac delta distribution as forcing term. This demonstrates that PDE problems with a non-smooth source term necessarily have degraded convergence order compared to problems with smooth right-hand sides and thus can be most efficiently solved by low-order FEM such as linear Lagrange elements.en_US
dc.description.urihttps://www.comsol.com/paper/fem-convergence-for-pdes-with-point-sources-in-2-d-and-3-d-26022en_US
dc.format.extent6 pagesen_US
dc.genreTechnical Reporten_US
dc.identifierdoi:10.13016/M2BG2HF0C
dc.identifier.citationGobbert, M., Kalayeh, K. M., Graf, J. S. FEM Convergence for PDEs with Point Sources in 2-D and 3-D. Presented at COMSOL Conference 2015, Boston, MA..
dc.identifier.urihttp://hdl.handle.net/11603/11553
dc.language.isoen_USen_US
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Mechanical Engineering Department Collection
dc.relation.ispartofUMBC Mathematics and Statistics Department
dc.relation.ispartofUMBC Faculty Collection
dc.relation.ispartofUMBC Student 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.subjectPoisson equationen_US
dc.subjectPoint Sourceen_US
dc.subjectDirac delta distributionen_US
dc.subjectconvergence studyen_US
dc.subjectmesh re finementen_US
dc.subjectUMBC High Performance Computing Facility (HPCF)en_US
dc.titleFEM Convergence for PDEs with Point Sources in 2-D and 3-Den_US
dc.typeTexten_US

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