Abstract
A paper which purports to make a comparison between finite difference and finite element methods is doomed to be met with much criticism. The reason for this inevitable fate is that a study such as this must contain a high degree of subjectivity which many readers will have cause to disagree with. Issues such as ulterior motives of the author, the proficiency of a computer programmer, the blurring of features which distinguish finite element from finite difference methods and the reader’s own biases or preferences make presentation of a satisfactorily complete and inoffensive comparison of these two numerical techniques virtually impossible.
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References
Shoup, T.E., A Practical Guide to Computer Methods for Engineers, Prentice-Hall, Englewood Cliffs, NJ (1978).
Holly, Jr., F.M., and A. Preissman, Accurate calculation of transport in two-dimensions, J. Hydr. Div. ASCE, 103, (1977) 1259–1277.
Peaceman, D.W., and H.H. Rachford, Jr., The numerical solution of parabolic and elliptic differential equations, J. Soc. Ind. Appl. Math., 3, (1955) 28–41.
Leendertse, J.J., Aspects of a Computational Model for Long-Period Water-Wave Propagation, Rand Memorandum RM-5294-PR, Santa Monica, CA (1967).
Zienkiewicz, O.C., The Finite Element Method, 3rd ed., McGraw-Hill, London (1977).
Finlayson, B.A., The Method of Weighted Residuals and Variational Principles, Academic Press, NY (1972).
Shapiro, A., and G.F. Pinder, Analysis of an upstream weighted collocation approximation to the transport equation, J. Comp. Phys., 39, (1981) 46–71.
Hayes, L., G. Pinder, and M. Celia, Alternating-direction collocation for rectangular regions, Comp. Meth. Appl. Mech. and Engrg., 27, (1981) 265–277.
Pinder, G.F. and W.G. Gray, Finite Element Simulation in Surface and Subsurface Hydrology, Academic Press, NY (1977).
Lewis, R.W. and P.M. Roberts, The finite element method for porous media flow, in Fundamentals of Transport Phenomena in Porous Media. ed. by J.Bear and M.Y. Corapcioglu, M. Nijhoff (1984).
Thompson, J.F. (ed.), Proceedings of the Symposium on the Numerical Generation of Curvilinear Coordinate Systems and Use in the Numerical Solution of Partial Differential Equations, Elsevier (1982).
Lynch, D.R. and W.G. Gray, Finite element simulation, of flow in deforming regions, J. Comp. Phys., 36, (1980) 135–153.
Hayes, L.J., R.P. Kendall and M.F. Wheeler, The treatment of sources and sinks in steady-state reservoir engineering simulations,” in Advances in Computer Methods for Partial Differential Equations, IMACS (1977).
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© 1984 Martinus Nijhoff Publishers, Dordrecht
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Gray, W.G. (1984). Comparison of Finite Difference and Finite Element Methods. In: Bear, J., Corapcioglu, M.Y. (eds) Fundamentals of Transport Phenomena in Porous Media. NATO ASI Series, vol 82. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6175-3_18
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DOI: https://doi.org/10.1007/978-94-009-6175-3_18
Publisher Name: Springer, Dordrecht
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