Uniformly convergent finite element methods for singularly perturbed parabolic partial differential equations

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dc.contributor.advisorStynes, Martinen
dc.contributor.authorGuo, Wen
dc.date.accessioned2014-08-28T09:01:21Z
dc.date.available2014-08-28T09:01:21Z
dc.date.issued1993
dc.date.submitted1993
dc.description.abstractThis thesis is concerned with uniformly convergent finite element methods for numerically solving singularly perturbed parabolic partial differential equations in one space variable. First, we use Petrov-Galerkin finite element methods to generate three schemes for such problems, each of these schemes uses exponentially fitted elements in space. Two of them are lumped and the other is non-lumped. On meshes which are either arbitrary or slightly restricted, we derive global energy norm and L2 norm error bounds, uniformly in the diffusion parameter. Under some reasonable global assumptions together with realistic local assumptions on the solution and its derivatives, we prove that these exponentially fitted schemes are locally uniformly convergent, with order one, in a discrete L∞norm both outside and inside the boundary layer. We next analyse a streamline diffusion scheme on a Shishkin mesh for a model singularly perturbed parabolic partial differential equation. The method with piecewise linear space-time elements is shown, under reasonable assumptions on the solution, to be convergent, independently of the diffusion parameter, with a pointwise accuracy of almost order 5/4 outside layers and almost order 3/4 inside the boundary layer. Numerical results for the above schemes are presented. Finally, we examine a cell vertex finite volume method which is applied to a model time-dependent convection-diffusion problem. Local errors away from all layers are obtained in the l2 seminorm by using techniques from finite element analysis.en
dc.description.statusNot peer revieweden
dc.description.versionAccepted Version
dc.format.mimetypeapplication/pdfen
dc.identifier.citationGuo, W. 1993. Uniformly convergent finite element methods for singularly perturbed parabolic partial differential equations. PhD Thesis, University College Cork.en
dc.identifier.urihttps://hdl.handle.net/10468/1637
dc.language.isoenen
dc.publisherUniversity College Corken
dc.relation.urihttp://library.ucc.ie/record=b1202593~S0
dc.rights© 1993, Wen Guo.en
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/en
dc.subjectPetrov-Galerkin finite element methodsen
dc.subjectStreamline diffusion schemeen
dc.subjectShishkin meshen
dc.subjectCell vertex finite volume methoden
dc.subject.lcshDifferential equations, Partialen
dc.thesis.opt-outfalse
dc.titleUniformly convergent finite element methods for singularly perturbed parabolic partial differential equationsen
dc.typeDoctoral thesisen
dc.type.qualificationlevelDoctoralen
dc.type.qualificationnamePhD (Science)en
ucc.workflow.supervisorcora@ucc.ie
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