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Finite element solutions to boundary value problems

dc.contributor.advisorFrederickson, Paul O.
dc.contributor.authorChew, Kok-Thai
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.subjectBoundary value problems
dc.titleFinite element solutions to boundary value problems
dc.typeThesis of Science Sciences University

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