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Finite element solutions to boundary value problems

dc.contributor.advisorFrederickson, Paul O.
dc.contributor.authorChew, Kok-Thai
dc.date.accessioned2017-06-06T13:40:15Z
dc.date.available2017-06-06T13:40:15Z
dc.date.created1977
dc.date.issued1977
dc.identifier.urihttp://knowledgecommons.lakeheadu.ca/handle/2453/2290
dc.description.abstractThe finite element solution of certain two-point boundary value problems is discussed. In order to obtain more accuracy than the linear finite element method can give, an order-h[superscript 4] global superconvergence technique is studied. This technique, which uses a quasi-inverse of the Rayleigh-Ritz-Galerkin (finite element) method, is motivated by the papers of C. de Boor and G. J. Fix [14] and P. 0. Frederickson [25]. The Peano kernel theorem is generalized and used to approximate the rate of convergence of the global superconvergence. Following Sard’s theory on best quadrature formulae [50], with some generalization, several quadrature formulae are derived. These quadrature formulae are shown to be consistent, and have some advantages over those obtained by Herbold, Schultz and Varga [34]. For solution of large linear systems which result from the finite element method, LU decomposition (Gaussian Elimination Method) is fast and accurate. However, when it comes to a singular or a nearly singular system, LU decomposition fails. The algorithm FAPIN developed by P. 0. Frederickson for 2-dimensional systems is able to solve singular systems as we demonstrate. We found FAPIN will work more efficiently in 1-dimensional case if we replace the DB[subscript q] approximate inverse C, developed by Benson [3], with other approximate inverses. For the sake of verifying the theory, appropriate numerical experiments are carried out.
dc.language.isoen_US
dc.subjectBoundary value problems
dc.titleFinite element solutions to boundary value problems
dc.typeThesis
etd.degree.nameMaster of Science
etd.degree.levelMaster
etd.degree.disciplineMathematical Sciences
etd.degree.grantorLakehead University


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