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A class of Petrov-Galerkin finite element methods is proposed for the numerical solution of the n dimensional stationary convection-diffusion equation. After an initial review of the literature we describe this class of methods and present both asymptotic and nonasymptotic error analyses. Links are made with the classical Galerkin finite element method and the cell vertex finite volume method. We then present numerical results obtained for a selection of these methods applied to some standard test problems. We also describe extensions of these methods which enable us to solve accurately for derivative values of the solution.

In this thesis, an integral representation theorem is obtained for non-negative solutions of the heat equation on X = (//R)('n-1) x (0,(INFIN)) x (0,T) and their boundary behaviour is investigated by using the abstract Fatou-Naim-Doob theorem. The boundary behaviour of positive solutions of the equation Lu = 0 on Y = (//R)('n) x (0,T), where L is a uniformly parabolic second-order differential operator in divergence form is also studied. / In particular, the notion of semi-thinness is introduced for the corresponding potential theories on X and Y and relationships between fine, semi-fine and parabolic limits are obtained. / Results of Kemper specialised to X are obtained by means of fine convergence and a Carleson-type local Fatou theorem is obtained for solutions of Lu = 0 on a union of parabolic regions.

Bibliography: leaves 110-115. / iv, 115 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Pure Mathematics, 1999

Thesis (Ph.D.)--York University, 2005. Graduate Programme in Mathematics and Statistics. / Typescript. Includes bibliographical references (leaves 69-75). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:NR11585

Thesis ( Ph.D. ) -- McMaster University, 1997. / Includes bibliographical references (leaves 63-66). Also available via World Wide Web.

Thesis (Ph.D.)--McMaster University (Canada), 1996. / Source: Dissertation Abstracts International, Volume: 57-10, Section: B, page: 6300. Adviser: H. P. Heinig.

Diss. Östersund : Mittuniversitetet, 2008.

Thesis (Ph.D.) -- University of Adelaide, Dept. of Pure Mathematics, 1999. / Bibliography: leaves 110-115.

Thesis (Ph.D.)--University of Adelaide, Dept. of Applied Mathematics, 2001. / Includes bibliographical references (leaves 158-163).