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References
Crandall, S H, "Engineering Analysis", McGraw Hill, New York. 1956.
Collatz, L, "The numerical treatment of differential equations", Springer-Verlag, Berlin 1960.
Anderssen, R S and Mitchell, A R, The Petrov-Galerkin method, Numerical Analysis Report 21. University of Dundee. 1977.
Wachspress, E L, "A rational finite element basis", Academic Press, New York, 1975.
Mitchell, A R and Wait, R, "The finite element method in partial differential equations", Wiley, London. 1977.
Hemker, P W, "A numerical study of stiff two-point boundary problems", Mathematisch Centrum, Amsterdam. 1977.
Griffiths, D F and Lorentz, J, "An analysis of the Petrov-Galerkin finite element method applied to a model problem", Research Paper 334, The University of Calgary. 1977.
Christie, I, Griffiths, D F, Mitchell, A R and Zienkiewicz, O C, "Finite element methods for second order differential equations with significant first derivatives", Int. J. for Num. Meths. in Engng. 10, 1389–1396. 1976.
Douglas, J, Dupont, T, and Wheeler, M F, "H1-Galerkin methods for the Laplace and heat equations", Math. aspects of finite elements. ed. C de Boor, Academic Press, New York 1974.
Lawlor, F M M, "The Galerkin method and its generalisations", M.Sc. Thesis, University of Dundee. 1976.
de Boor, C R, "The method of projections as applied to the numerical solution of two point boundary value problems using cubic splines", Ph.D. Thesis, University of Michigan. 1966.
Lucas, T R and Reddien, G W, "A high order projection method for nonlinear two point boundary value problems", Numer. Math. 20, 257–270. 1973.
Rachford, H H and Wheeler, M F, "An H−1 Galerkin procedure for the two point boundary value problem", Maths aspects of finite elements, ed. C de Boor, Academic Press, New York. 1974.
Heinrich, J C, Huyakorn, P S, Zienkiewicz, O C and Mithcell, A R, "An upwind finite element scheme for two dimensional convective transport equation", Int. J. for Num. Meths. in Engng, 11, 131–143. 1977.
Heinrich, J C and Zienkiewicz, O C, "Quadratic finite element schemes for two dimensional convective-transport problems", Int. J. for Num. Meths. in Engng. (to appear).
Price, H S, Varga, R S and Warren, J E, "Application of oscillation matrices to diffusion-convection equations", J. Math. Phys. 45, 1966.
Price, H S, Cavendish, J C and Varga, R S, "Numerical methods of high-order accuracy for diffusion-convection equations", J. of Soc. Pet. Eng. 1963.
Price, H S and Varga, R S, "Approximations of parabolic problems with applications to petroleum reservoir mechanics", SIAM AMS Proc 2, 1970.
Siemieniuch, J L and Gladwell, I, "Some explicit finite-difference methods for the solution of a model diffusion-convection equation", Numerical Analysis Report 16, University of Manchester. 1976.
Gresho, P M, Lee, R L and Sani, R L, "Advection dominated flows with emphasis on the consequence of mass lumping", ICCAD Second International Symposium on Finite Element Methods in Flow Problems, S Margherita Ligure Italy. 1976.
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Mitchell, A.R., Griffiths, D.F. (1978). Generalised Galerkin methods for second order equations with significant first derivative terms. In: Watson, G.A. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 630. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067699
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DOI: https://doi.org/10.1007/BFb0067699
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