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

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dc.contributor.advisor Stynes, Martin en
dc.contributor.author Guo, Wen
dc.date.accessioned 2014-08-28T09:01:21Z
dc.date.available 2014-08-28T09:01:21Z
dc.date.issued 1993
dc.date.submitted 1993
dc.identifier.citation Guo, W. 1993. Uniformly convergent finite element methods for singularly perturbed parabolic partial differential equations. PhD Thesis, University College Cork. en
dc.identifier.uri http://hdl.handle.net/10468/1637
dc.description.abstract This 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.format.mimetype application/pdf en
dc.language.iso en en
dc.publisher University College Cork en
dc.relation.uri http://library.ucc.ie/record=b1202593~S0
dc.rights © 1993, Wen Guo. en
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/ en
dc.subject Petrov-Galerkin finite element methods en
dc.subject Streamline diffusion scheme en
dc.subject Shishkin mesh en
dc.subject Cell vertex finite volume method en
dc.subject.lcsh Differential equations, Partial en
dc.title Uniformly convergent finite element methods for singularly perturbed parabolic partial differential equations en
dc.type Doctoral thesis en
dc.type.qualificationlevel Doctoral en
dc.type.qualificationname PhD (Science) en
dc.internal.availability Full text available en
dc.check.info No embargo required en
dc.description.version Accepted Version
dc.description.status Not peer reviewed en
dc.internal.school Mathematics en
dc.check.type No Embargo Required
dc.check.reason No embargo required en
dc.check.opt-out Not applicable en
dc.thesis.opt-out false
dc.check.embargoformat Not applicable en
ucc.workflow.supervisor cora@ucc.ie


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© 1993, Wen Guo. Except where otherwise noted, this item's license is described as © 1993, Wen Guo.
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