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dc.contributor.authorElman, Howard C.en_US
dc.contributor.authorRamage, Alisonen_US
dc.date.accessioned2004-05-31T23:02:40Z
dc.date.available2004-05-31T23:02:40Z
dc.date.created2000-03en_US
dc.date.issued2000-03-23en_US
dc.identifier.urihttp://hdl.handle.net/1903/1061
dc.description.abstractIt is well known that discrete solutions to the convection-diffusion equation contain nonphysical oscillations when boundary layers are present but not resolved by the discretisation. However, except for one-dimensional problems, there is little analysis of this phenomenon. In this paper, we present an analysis of the two-dimensional problem with constant flow aligned with the grid, based on a Fourier decomposition of the discrete solution. For Galerkin bilinear finite element discretisations, we derive closed form expressions for the Fourier coefficients, showing them to be weighted sums of certain functions which are oscillatory when the mesh P\'{e}clet number is large. The oscillatory functions are determined as solutions to a set of three-term recurrences, are then used to characterise the oscillations of the discrete solution in terms of the mesh P\'{e}clet number and boundary conditions of the problem. (Also cross-referenced UMIACS-TR-2000-15)en_US
dc.format.extent782269 bytes
dc.format.mimetypeapplication/postscript
dc.language.isoen_US
dc.relation.ispartofseriesUM Computer Science Department; CS-TR-4118en_US
dc.relation.ispartofseriesUMIACS; UMIACS-TR-2000-15en_US
dc.titleA Characterisation of Oscillations in the Discrete Two-Dimensional Convection-Diffusion Equationen_US
dc.typeTechnical Reporten_US
dc.relation.isAvailableAtDigital Repository at the University of Marylanden_US
dc.relation.isAvailableAtUniversity of Maryland (College Park, Md.)en_US
dc.relation.isAvailableAtTech Reports in Computer Science and Engineeringen_US
dc.relation.isAvailableAtUMIACS Technical Reportsen_US


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